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THE  INTERNATIONAL  SCIEWIFI 


SIG- 


AN  EXPOSITION  OF  THE  PRINCIPLES 


OF 


MONOCULAR  AND  BINOCULAR  VISION. 


BY 

JOSEPH   LE   CONTE,  LL.  D., 

•==^" 

ACTH.OR  OF  "ELEMENTS  OF  GEOLOGY,"  "RELIGION  AND  SCIENCE,"  AND  PROPES:OE  OP 
GEOLOGY  AND  NATtfKAL  HISTORY  IN  THE  UNIVERSITY  OF  CALIFORNIA. 


WITH  NUMEROUS  ILLUSTRATIONS. 


NEW  YORK: 

D.  APPLETON    AND    COMPANY, 
1,  3,  AND  5   BOND   STREET. 

1881. 


COPYRIGHT   BY 

D.  APPLETON  AND  COMPANY. 

1881. 


PKEFACE. 


IN  writing  this  treatise  I  have  tried  to  make  a  book 
that  would  be  intelligible  and  interesting  to  the  thought- 
ful general  reader,  and  at  the  same  time  profitable  to 
even  the  most  advanced  specialist  in  this  department. 
I  find  justification  for  the  attempt  in  the  fact  that  there 
is  not,  to  my  knowledge,  any  work  covering  the  same 
ground  in  the  English  language.  Vision  has  been 
treated  either  as  a  branch  of  optics  or  else  as  a  branch 
of  physiology  of  the  nervous  system.  Helmholtz's  great 
work  on  "  Physiological  Optics,"  of  whiqji  there  exist 
both  a  German  and  a  French  edition,  is  doubtless  ac- 
cessible to  scientists,  but  this  work  is  so  technical  that 
it  is  practically  closed  to  all  but  the  specialist.  I  /be- 
lieve, therefore,  that  the  work  which  I  now  offer  meets 
a  real  want,  and  fills  a  real  gap  in  scientific  literature. 

The  form  in  which  the  subject  is  here  presented 
has  been  developed  entirely  independently,  and  as  the 
result  of  a  conscientious  endeavor  to  make  it  clear  to 
students  under  my  instruction.  As  evidence  of  this,  I 
would  draw  attention  to  the  fact  that,  out  of  one  hun- 
dred and  thirty  illustrations,  only  about  twelve  have 

361 


4  •       PREFACE. 

been  taken  from  other  writers.  On  those  points  in 
which  I  differ,  not  only  in  form  but  in  matter,  from 
other  writers,  I  am  willing  to  abide  the  judgment  of 
those  best  qualified  to  decide. 

I  have  devoted  a  large,  perhaps  some  may  think  a 
too  large,  space  to  the  discussion  of  binocular  vision. 
I  have  done  so,  partly  because  I  have  devoted  special 
attention  to  this  department,  partly  because  it  is  so  very 
imperfectly  presented  by  other  writers,  but  chiefly  be- 
cause it  seemed  to  me  by  far  the  most  fascinating  por- 
tion of  the  whole  subject  of  vision. 

As  a  means  of  scientific  culture,  the  study  of  vision 
seems  to  me  almost  exceptional.  It  makes  use  of,  and 
thus  connects  together,  the  sciences  of  Physics,  Physi- 
ology, and  even  Psychology.  It  makes  the  cultivation 
of  the  habit  of  observation  and  experiment  possible  to 
all;  for  the  greatest  variety  of  experiments  may  be 
made  without  expensive  apparatus,  or,  indeed,  appa- 
ratus of  any  kind.  And,  above  all,  it  compels  one  to 
analyze  the  complex  phenomena  of  Sense  in  his  own 
person,  and  is  thus  a'  truly  admirable  preparation  for 
the  more  difficult  task  of  analysis  of  those  still  higher 
and  more  complex  phenomena  which  are  embraced  in 
the  science  of  Psychology. 

BERKELEY,  CALIFORNIA,  May  20,  1880. 


ANALYTICAL  TABLE  OF  CONTENTS. 


INTRODUCTORY. 

PAGE 

THE  RELATION  OF  GENERAL  SENSIBILITY  TO  SPECIAL  SENSE  .        9 

Law  of  differentiation,  10 ;  gradation  among  the  senses,  11 ;  in 
kind  of  contact,  13 ;  in  distance  of  perception,  13 ;  in  refine- 
ment of  organ,  14. 

PART  I. 

MONOCULAR  VISION. 
CHAPTER  I. 

GENERAL  STRUCTURE  OF  THE  HUMAN  EYE,  AND  THE  FOR- 
MATION OF  IMAGES .  .  .  .  .  17 

SECTION  I.— GENERAL  STRUCTURE  :  General  form  and  setting,  17 ; 
illustrations,  18 ;  the  muscles,  18  ;  illustrations  of  their  action, 
19 ;  the  eyeball,  20 ;  sclerotic,  20 ;  cornea,  21 ;  iris,  21 ;  lin- 
ings, 22 ;  choroid,  22 ;  ciliary  musc]e,  22 ;  retina,  22 ;  con- 
tents of  ball,  23  ;  lens,  23  ;  humors,  24. 

SECTION  II. — FORMATION  OF  THE  IMAGE,  24;  conditions  of  per- 
fect image,  25 ;  experiment,  27 ;  illustrations,  27 ;  property 
of  a  lens,  27 ;  proofs  of  a  retinal  image,  29  ;  nodal  point,  29. 

CHAPTER  II. 

THE  EYE  AS  AN  OPTICAL  INSTRUMENT          .  .  .30 

Comparison  with  the  camera,  30 ;  chromatism,  31 ;  correction  of 
chromatism,  31 ;  aberration,  35  ;  correction  of  aberration,  36  ; 
adjustment  for  light,  37 ;  adjustment  for  distance,  40 ;  accom- 
modation of  the  eye,  42 ;  experiment  illustrating,  42 ;  theory 
of  adjustment,  44;  Helmholtz's  view,  44. 


6  ANALYTICAL  TABLE   OF  CONTENTS. 

CHAPTER  III. 

PAGE 

DEFECTS  OF  THE  EYE  AS  AN  INSTRUMENT      .  .  .46 

Emrnetropy,  or  normal  sightedness,  46  ;  myopy,  or  near-sighted- 
ness, 46 ;  presbyopy,  or  old-sightedness,  48  ;  hypermetropy, 
or  long-sightedness,  51 ;  astigmatism,  52. 

CHAPTER  IV. 

EXPLANATION  OF  PHENOMENA  OF  MONOCULAR  VISION         .       53 

SECTION  I. — STRUCTURE  OF  RETINA,  53 ;  optic  nerve,  54 ;  relations 
to  the  eye,  54 ;  layers  of  retina,  55 ;  bacillary  layer,  55 ;  cen- 
tral spot,  57 ;  blind  spot,  59  ;  perception  of  color,  59  ;  primary 
colors,  60 ;  view  of  Brewster,  60 ;  of  Young,  60 ;  of  Hering, 
60 ;  theory  of  color-perception,  61 ;  theory  of  Young,  61 ;  of 
Hall,  61 ;  color-blindness,  62 ;  theory  of,  63. 

SECTION  II. — FUNCTIONS  OF  THE  RETINA  :  Law  of  outward  pro- 
jection of  retinal  impressions,  64 1  compared  with  other  senses, 
65 ;  illustrations  of  this  property,  66  ;  phosphenes,  67 ;  muscse 
volitantes,  67 ;  Purkinje's  figures,  68 ;  ocular  spectra,  69 ; 
corresponding  points,  retinal  and  spatial,  72;  properties  of 
the  central  spot,  73  |  function  of  the  central  spot,  74 ;  mini- 
mum visible,  76 ;  minimum  tactile,  77  ;  blind  spot,  78 ;  ex- 
periments illustrating,  78-81 ;  why  there  is  no  visible  repre- 
sentative of  this  spot  in  field  of  view,  82 ;  erect  vision,  83  ; 
comparison  with  other  senses,  84 ;  explained  by  law  of  direc- 
tion, 85 ;  illustrations  of  this  law,  86. 

PART  II. 

BINOCULAR    VISION. 

CHAPTER  I. 
SINGLE  AND  DOUBLE  IMAGES  .  .  .  .  .90 

The  two  eyes  as  one  instrument,  90 ;  the  binocular  field,  91 ; 
double  images,  92  ;  experiments  illustrating,  92-94 ;  analogy 
with  sense  of  touch,  95 ;  single  vision,  95 ;  corresponding 
points  of  the  two  retinas,  96 ;  law  of  corresponding  points, 
97  ;  conditions  of  single  vision,  99 ;  horopter,  101 ;  optic  chi- 
asm,  and  its  relation  to  the  law  of  corresponding  points,  101 ; 
theories  of  the  origin  of  property  of  corresponding  points, 
102 ;  nativistic  theory,  103 ;  empiristic  theory,  103 ;  consen- 
sual adjustments,  104 ;  two  fundamental  laws,  105. 

CHAPTER  II. 

SUPERPOSITION  OF  EXTERNAL  IMAGES  .  .  .107 

Of  the  same  object,  107  ;  of  different  objects,  108 ;  Case  1 .  Dis- 
similar objects,  103  ;  experiments  illustrating,  108-109  ;  Case 


ANALYTICAL   TABLE   OF  CONTENTS. 


2.  Similar  objects,  112  ;  experiments  illustrating,  112-113 ; 
Case3.  Many  similar  objects  regularly  arranged,  115;  experi- 
ments illustrating,  115 ;  dissociation  of  consensual  adjust- 
ments, 117 ;  experiment  illustrating,  118 ;  general  conclu- 
sions, 118. 

CHAPTER  III. 
BINOCULAR  PERSPECTIVE       '  .  .  .  .  .     120 

Experiments  illustrating,  120-123  ;  stereoscopy,  125  ;  stereoscopic 
pictures,  126 ;  how  taken,  127 ;  combination  of  stereoscopic 
pictures,  128  ;  with  the  naked  eyes,  128  ;  experiments  illus- 
trating, 129-133 ;  combination  by  the  use  of  the  stereoscope, 
134;  inverse  perspective,  135;  experiments  illustrating,  136- 
141 ;  different  forms  of  perspective,  142  ;  aerial,  142  ;  mathe- 
matical, 142  ;  monocular  or  focal,  142 ;  binocular,  143. 

CHAPTER  IV. 
THEORIES  OF  BINOCULAR  PERSPECTIVE  .  .  .     145 

Wheatstone's  theory,  145  ;  Brucke's  theory,  147  ;  Dove's  experi- 
ment, 148 ;  my  own  view,  151 ;  return  to  comparison  of  the 
eye  with  the  camera,  152. 

CHAPTER  V. 

JUDGMENT  OF  DISTANCE,  SIZE,  AND  FORM     ,  .  156 

Judgment  of  distance,  156  ;  different  modes  of,  156  ;  size,  157 ;  ex- 
periments illustrating,  158, 159 ;  form,  1 60 ;  outline  form,  160 ; 
solid  form,  160 ;  gradation  of  judgments,  160 ;  retrospect,  162. 


PART  III. 
ON  SOME  DISPUTED  POINTS  IN  JBINOCULAK  VISION. 

CHAPTER  I. 
LAWS  OF  OCULAR  MOTION      .....    164 

SECTION  I. — LAWS  OF  PARALLEL  MOTION  :  Listing's  law,  164 ; 
experiments  illustrating,  164-172 ;  the  statement  of  the  laws, 
173;  contrary  statement  by  Helmholtz  explained,  175;  rota- 
tion on  optic  axes  in  parallel  motion  only  apparent,  176. 

SECTION  II. — LAWS  OF  CONVERGENT  MOTION,  177 ;  the  rotation 
in  this  case  real,  178 ;  difficulty  in  experimenting,  178 ;  ex- 
periments proving  rotation  on  optic  axes  in  convergence, 
180-187 ;  effect  of  elevation  and  depression  of  visual  plane, 
188 ;  experiments  illustrating,  188  ;  cause  of  the  rotation, 
189  ;  laws  of  parallel  and  convci'gent  motion  contrasted,  189. 


8  ANALYTICAL  TABLE   OF  CONTENTS. 

CHAPTER  II. 

PAGE 

THE  HOROPTER  .  .  .  .  .  .192 

Defined,  192 ;  difference  of  opinion  as  to  its  nature,  193 ;  Muller'.s 
horopteric  circle,  194;  Claparede's  view,  194;  Helmholtz's 
results,  195 ;  Helmholtz's  view  as  to  the  relation  of  apparent 
and  real  vertical  meridian,  197  ;  experiments  testing  its  truth, 
198 ;  adverse  conclusion  reached,  201  ;  Meissner's  results, 
experiments  proving,  203 ;  my  results  confirm  Meissner's, 
206 ;  experiments  proving,  206-210 ;  conclusions  in  regard  to 
the  horopter,  210 ;  wherein  I  differ  from  Meissner,  211. 

CHAPTER  III. 

ON  SOME  FUNDAMENTAL  PHENOMENA  OF  BINOCULAR  VISION 
USUALLY  OVERLOOKED,  AND  ON  A  NEW  MODE  OF  DlA- 

GRAMMATIO  REPRESENTATION   BASED    THEREON    .  .       213 

Usual  mode  of  representation  untrue,  213 ;  experiments  illustrat- 
ing, 214  ;  heteronymous  shifting  of  the  two  fields  of  view  and 
experiments  illustrating,  216-221;  ceil  cyclopienne,  217,  222; 
first  law  or  law  of  heteronymous  shifting  stated,  223 ;  ho- 
monymous  rotation  of  the  two  fields,  224 ;  experiments  illus- 
trating, 224-227 ;  second  law  or  law  of  homonymous  rotation 
stated,  228 ;  statement  of  the  two  laws,  229 ;  determination 
of  the  interocular  space,  230  ;  experiments  illustrating  the 
necessity  of  the  new  mode,  231-237  ;  application  of  the  new 
mode  to  representation  of  stereoscopic  phenomena,  238.  Some 
curious  phenomena  resulting  from  the  heteronymous  shift- 
ing *of  the  fields  of  view,  245 ;  to  trace  the  outline  of  a  picture 
where  it  is  not,  245 ;  to  trace  the  outline  of  a  candle-flame  on 
an  opaque  screen,  248 ;  to  see  through  a  book  or  a  deal  board, 
250. 

CHAPTER  IV. 

VISUAL  PHENOMENA  IN  OCULAR  DIVERGENCE  .  .    252 

1.  In  drowsiness,  252;  2.  In  other  modes  of  producing  diver- 
gence, 255;  3.  Prevalence  of  law  of  corresponding  points  over 
law  of  direction,  258  ;  diagrams  illustrating,  259. 

CHAPTER  V. 

COMPARATIVE  PHYSIOLOGY  OF  BINOCULAR  VISION   .  .    262 

Optic  chiasm  in  lower  animals,  262 ;  divergence  of  eye-sockets, 
263 ;  when  extreme,  incompatible  with  binocular  vision,  264 ; 
central  spot,  266 ;  how  far  it  exists  in  lower  animals,  267 ; 
importance  of  this  spot,  267 ;  general  changes  in  the  eye  as 
we  go  up  the  vertebrate  scale,  269. 


SIGHT. 


INTKODUCTOKY. 

RELATION  OF  GENERAL  SENSIBILITY  TO  SPECIAL 

SENSE. 

SENSOEY  nerve-fibers  are  cylindrical  threads  of  mi- 
croscopic fineness,  terminating  outwardly  in  the  sensi- 
tive surfaces  and  sense-organs,  and  inwardly  in  the 
nerve-centers,  especially  the  brain.  Impressions  on 
their  outer  extremity  are  transmitted  along  the  fiber 
with  a  velocity  of  about  one  hundred  feet  per  second, 
and  determine  changes  in  the  nerve-centers,,  which  in 
turn  may  determine  changes  in  consciousness,  which  we 
call  sensation.  The  simplest  and  most  general  form  of 
sensation  is  what  is  called  general  sensibility,  or  common 
sensation.  This  is  a  mere  sense  of  contact,  an  indefinite 
response  to  external  impression.  It  gives  knowledge  of 
externality — of  the  existence  of  the  external  world — 
but  not  of  the  properties  of  matter.  The  lowest  animals 
possess  this,  and  nothing  more.  But,  as  we  go  up  the 
scale  of  animals,  in  order  to  give  that  wider  and  more 
accurate  knowledge  of  the  various  properties  of  matter 
necessary  for  the  complex  relations  of  the  higher  ani- 
mals, sensory  nerve-fibers  are  differentiated  into  several 
kinds,  so  that  each  may  give  clear  knowledge  of  differ- 


10  INTRODUCTORY. 

ent  properties.  Thus,  for  example,  the  first  pair  of 
cranial  nerves — olfactive — is  specially  organized  to  take 
cognizance  of  certain  impressions,  called  smells,  and  no- 
thing else.  If,  therefore,  these  nerve-fibers  are  irritated 
in  any  way,  even  mechanically,  by  scratching  or  pinch- 
ing, they  do  not  feel  but  perceive  an  odor.  The  second 
pair  of  cranial  nerves — the  optic — is  specially  organized 
in  a  truly  wonderful  way  to  respond  to  the  ethereal 
vibrations  called  light,  and  nothing  else.  If,  therefore, 
these  nerves  be  mechanically  irritated,  we  do  not  feel 
anything,  but  see  a  flash  of  light.  In  a  similar  manner, 
the  eighth  pair — auditive  nerve — is  specially  organized 
to  respond  to  sound-vibrations,  and  nothing  else ;  and 
therefore  mechanical  irritation  of  this  nerve  produces 
only  the  sensation  of  sound.  Similarly,  the  ninth  pair, 
or  gustative  nerve,  is  organized  for  the  appreciation  of 
taste  only;  and,  therefore,  a  feeble  electric  current 
through  this  nerve  produces  a  peculiar  taste. 

We  have  in  these  facts  only  an  example  of  a  very 
wide  law,  viz.,  the  law  of  differentiation.  In  the  lowest 
animals  all  the  tissues  and  organs  which  are  so  widely 
distinct  in  the  higher  animals  are  represented  by  an 
unmodified  cellular  structure,  performing  all  the  func- 
tions of  the  animal  body,  but  in  an  imperfect  manner. 
Each  cell  in  such  an  organism  will  feel  like  a  nervous 
cell,  contract  like  a  muscular  cell,  respire  like  a  lung- 
cell,  or  digest  like  a  stomach-cell.  As  we  go  up  the  ani- 
mal scale,  this  common  structure  is  differentiated  first 
into  three  main  systems,  viz.,  the  nutritive  or  epithelial 
system,  the  nerve-system,  and  the  blood-system  :  the  first, 
presiding  over  absorption  and  elimination,  i.  e.,  exchange 
of  matter  between  the  exterior  world  and  the  organism  ; 
the  second,  over  exchange  of  force  between  exterior 
and  interior  by  impressions  determining  changes  in 


RELATION   OF  GENERAL  TO   SPECIAL  SENSE.         H 

consciousness,  and  by  will  determining  changes  in  exter- 
nal phenomena ;  the  third,  presiding  over  exchanges  be- 
tween different  parts  of  the  organism.  The  first  kind 
of  exchange  may  be  likened  to  foreign  commerce ;  the 
second,  to  exchange  of  intelligence  by  telegraphic  com- 
munication with  foreign  countries ;  the  third,  to  the 
internal  carrying  trade.  These  three  systems  are  very 
early  differentiated  in  the  embryo,  since  they  are  sev- 
erally produced  from  the  three  primitive  layers  of  the 
germinal  disk,  viz.,  the  endoderm,,  the  ectoderm,  and 
the  mesoderm. 

Neglecting  now  all  but  the  second  or  nervous  sys- 
tem as  we  still  go  up,  this  is  again  differentiated  into 
three  sub-systems,  viz.,  the  conscio-vohmtary ',  or  sensori- 
molor,  the  reflex,  and  the  ganglionic,  each  with  its 
center  and  its  afferent  and  efferent  fibers.  Neglecting, 
again,  the  two  others,  and  selecting  only  the  sensori- 
motor,  the  sensory  fibers  of  this  sub-system  are  again 
differentiated  into  five  kinds,  each  to  respond  to  a  dif- 
ferent kind  of  impression,  and  perceive  a  different  prop- 
erty, viz.,  the  five  special  sense-fibers  for  sight,  hear- 
ing, smell,  taste,  and  touch.  Even  these  are  probably 
again  further  differentiated ;  for  the  perception  of  dif- 
ferent colors  and  different  musical  sounds  is  probably 
effected  by  means  of  special  fibers  of  the  optic  and  au- 
ditive nerves.  The  following  diagram  (Fig.  1)  illus- 
trates these  successive  differentiations. 

Gradation  among  the  Senses.— Now  all  these  higher 
special  senses  may  be  regarded  as  the  result  of  refine- 
ments of  common  sensation — each  a  more  refined  touch. 
Coarse  vibrations  are  perceived  by  the  nerves  of 
mon  sensation  as  a  jarring.  When  the  vibrations 
so  rapid  that  there  are  sixteen  complete  movem 
back  and  forth  in  a  second,  an  entirely  different  sensa- 

v 


12 


INTRODUCTORY. 


tion  is  produced,  which  we  call  sound.  The  vibrations 
are  no  longer  perceived  by  the  nerves  of  common  sen- 
sation, but  a  special  nerve — the  auditive — is  organized  to 
respond  to  or  co-vibrate  with  them.  As  the  vibrations 
increase  in  number,  they  are  perceived  as  higher  and 
higher  pitch,  until  they  reach  the  number  of  about 


FIG.  1. 


UNMOlDiriED 

CELLULAR  [STRUCTURE 


40,000  in  a  second.  This  is  the  highest  pitch  the  ear 
can  perceive,  the  quickest  vibrations  the  auditive  nerve 
can  respond  to.  Beyond  this  there  is  absolute  silence, 
but  only  because  we  have  no  nerve  organized  to  co- 
vibrate  with  these  more  rapid  undulations.  These 
vibrations,  inaudible  to  us,  may  possibly  be  perceived  by 
some  lower  animals,  as,  for  example,  insects ;  we  can  not 


RELATION  OF  GENERAL  TO  SPECIAL  SENSE.  13 

tell.  After  a  long  interval,  vibrations  again  appear  in 
consciousness  as  light.  The  vibrations  which  produce 
this  sensation  are  so  rapid— 399,000,000,000,000  in  a  sec- 
ond— that  they  can  be  conveyed  only  by  the  ethereal 
medium.  For  the  perception  of  these  vibrations,  a  pe- 
culiar and  wonderful  organization  is  necessary,  found 
only  in  the  optic  nerve.  Above  the  number  just  given, 
ethereal  vibrations  are  perceived  as  different  colors,  in 
the  order  seen  in  the  spectrum,  until  831,000,000,000,- 
000  is  reached.  Beyond  this  we  have  no  nerve  capable 
of  responding. 

The  gradation  among  the  special  senses  may  be 
shown  in  a  different  way.  In  touch  we  require  direct 
and  usually  solid  contact ;  in  taste,  liquid  contact,  for 
unless  a  body  is  soluble  it  can  not  be  tasted ;  in  smelly 
the  contact  is  gaseous,  for  unless  a  body  is  volatile  or 
vaporizable  it  can  not  be  smelled.  In  this  last  case, 
the  perception  of  objects  at  a  distance  begins ;  still  it 
is  by  direct  contact,  for  particles  from  the  distant  body 
must  touch  the  olfactive  nerve.  In  hearing,  there  is 
no  contact  of  the  sounding  body,  but  the  vibrations  are 
conveyed  through  a  medium.  We  perceive  at  a  dis- 
tance, limited  only  by  the  extent  of  the  atmosphere  and 
the  energy  of  the  initial  vibration.  In  sight,  finally,  we 
perceive  objects  at  a  distance  which  is  illimitable,  the 
vibrations  being  conveyed  by  a  medium  which  is  uni- 
versal, and  too  subtile  to  be  recognized  except  as  the 
bearer  of  light. 

Again,  commencing  with  taste :  In  this  sense  we  dis- 
tinctly perceive  that  the  sensation  is  subjective — is  in 
us,  not  in  the  body  tasted.  In  smell,  there  is  an  equal 
commingling  of  subjectiveness  and  objectiveness.  We 
distinctly  perceive  the  sensation  as  in  the  nose,  and  yet 
by  experience  we  have  learned  to  refer  it  to  an  object 


14  INTRODUCTORY. 

at  a  distance.  In  hearing,  we  already  refer  the  cause 
so  completely  to  a  distant  object  that  there  is  but  the 
smallest  possible  remnant  of  a  consciousness  of  sensa- 
tion in  the  ear  j  the  sound  does  not  seem  to  be  in  the 
ear,  but  in  yonder  bell.  Finally,  in  sight,  the  impres- 
sion is  so  completely  projected  outward,  and  the  con- 
sciousness of  anything  taking  place  in  the  eye  so  com- 
pletely lost,  that  it  is  only  by  careful  analyses  that  we 
can  be  convinced  of  its  essential  subjectiveness. 

The  order  which  we  have  given  above  is  also  the 
order  of  increasing  specialization  and  refinement  of  the 
senses.  But  only  in  the  two  higher  senses — only  in 
those  senses  in  which  there  is  no  direct  contact,  but  the 
impressing  force  is  conveyed  by  means  of  vibration 
through  a  medium — only  in  these  highest  senses  do  we 
find  that,  besides  the  specialization  of  the  nerve-fibers 
to  respond  to  peculiar  vibrations,  also  an  elaborate  in- 
strument is  placed  in  front  of  the  specialized  nerve  in 
order  to  intensify  the  impression  and  give  it  more  defi- 
niteness.  It  is  wholly  by  virtue  of  this  supplementary 
instrument  that  we  are  able  to  hear  not  only  sound  but 
music,  or  to  see  not  only  light  but  objects.  The  lowest 
animals  in  which  an  optic  nerve  is  found  perceive  light, 
but  not  objects ;  because,  though  the  specialized  nerve  is 
present,  the  appropriate  instrument  is  wanting.  It  is 
on  these  two  higher  senses  that  fine  art  is  wholly  and 
science  is  mainly  founded.  The  specialized  nerve  and 
the  instrument  for  intensifying  and  making  definite  the 
impression  are  together  called  the  sense-organ.  It  is  of 
the  most  highly  specialized  of  these  nerves  and  the 
most  refined  of  these  instruments,  the  highest  of  the 
sense-organs,  the  eye,  that  we  are  now  about  to  treat. 

It  may  be  well  to  bear  in  mind  and  keep  distinct 
what  may  be  called  the  direct  gifts  of  sight,  and  what 


RELATION   OF   GENERAL  TO   SPECIAL   SENSE.          15 

are  added  by  the  mind  as  judgments  based  upon  these 
gifts.  The  direct  data  are  only  light,  its  intensity,  color, 
and  direction.  These  are  incapable  of  further  analysis, 
and  are  therefore  simple  sensations.  Outline  form  may 
possibly  be  added,  though  this  may  be  analyzed  into  a 
combination  of  directions.  But  solid  form,  size,  and 
distance,  though  they  may  seem  to  be  immediately  per- 
ceived, are  not  direct  perceptions,  but  only  very  simple 
judgments  based  on  the  data  given  above.  We  only 
state  these  facts  now  that  they  may  be  borne  in  mind. 
We  hope  to  substantiate  them  hereafter. 


PAET   I. 
MONOCULAR    VISION. 


CHAPTER  I. 

GENERAL   STRUCTURE   OF   THE  HUMAN  EYE,    AND   THE 
FORMATION  OF  IMAGES. 

SECTION1"  I.— GENERAL  STRUCTURE  OF  THE  EYE. 

General  Form  and  Setting.— The  eye  is  nearly  spheri- 
cal in  shape,  and  about  an  inch  in  diameter.  The  socket 
in  which  it  is  set  is  not  a  hollow  sphere,  but  an  irregular 
hollow  cone  or  pyramid.  Evidently,  therefore,  the 
deeper  and  smaller  parts  of  the  hollow  must  be  filled 
with  something  else.  It  is  filled  with  loose  connective 
tissue,  containing  fat.  On  this,  as  on  a  soft  cushion, 
the  eyeball  rolls  with  ease  in  every  direction.  The  eye 
proper  is  really  behind  the  skin,  or  outer  integument  of 
the  face,  for  the  skin  which  covers  the  lids  turns  over  the 
edge  (Fig.  2, 1 1)  and  passes  under  the  lids,  becoming  here 
thin  and  tender  mucous  membrane ;  it  is  then  reflected 
from  the  back  part  of  the  lid  to  the  anterior  surface  of 
the  white  portion  of  the  ball  (Fig.  2,  a  a\  then  passes  for-" 
ward  again  over  the  ball  as  far  as  the  clear  part,  or  cornea 
(Fig.  2,  c  c  c\  and  then  entirely  over  this,  although  very 
closely  attached.  If  carefully  dissected  off,  it  would  leave 


18 


MONOCULAR  VISION. 


the  eyeball  behind  it.  This  mucous  covering  of  the 
anterior  portion  of  the  eyeball  is  called  the  conjunctiva. 

Illustrations. — In  ordinary  inflammations  of  the  eye, 
it  is  this  mucous  membrane  which  is  affected,  and  not 
the  eye  proper.  Disease  of  the  eye  proper  is  a  far 
more  serious  matter. 

When  motes  get  into  the  eye,  they  can  not  go  be- 
yond easy  reach,  viz.,  beyond  the  reflection  of  the  mu- 
cous membrane,  from  the  lid  to  the  ball,  at  the  points  a  a. 

The  Muscles. — We  all  know  the  rapidity  and  preci- 
sion with  which  the  eye  turns  in  all  directions.  This 
is  by  means  of  six  slender  muscles.  Four  of  these  are 

FIG.  2. 


MUSCLE?  OF  THE  EYEBALL. — #,  optic  nerve;  5,  supe- 
rior oblique  muscle  ;  c,  pulley ;  d.  inferior  oblique. 
The  other  four  are  the  recti. 


called  the  straight  muscles,  and  two  the  oblique  muscles. 
The  straight  muscles  all  rise  at  the  bottom  of  the  con- 
ical socket,  diverge  as  they  pass  forward,  and  grasp 
the  eyeball  above,  below,  on  right  and  left  side,  just  in 
front  of  the  middle  or  equator  of  the  globe  (Fig.  3). 
They  are  called  severally  superior,  inferior,  external, 
and  internal  rectus.  The  first  turns  the  ball  upward, 
the  second  downward,  the  third  to  the  right,  and  the 
fourth  to  the  left,  if  we  are  speaking  of  the  right  eye. 
This  is  their  action  expressed  generally  ;  but,  by  refer- 
ence to  Fig.  20,  on  page  54,  it  is  seen  that  the  axis  of 


GENERAL  STRUCTURE  OF  THE  EYE.        19 

the  eye  is  not  coincident  with  the  axis  of  the  socket, 
and,  therefore,  the  action  of  the  superior  rectus  by  itself 
is  not  only  to  turn  the  eye  upward,  but  also  to  rotate 
it  a  little  on  its  axis  inward  toward  the  nose ;  while  the 
inferior  rectus  not  only  turns  the  eye  downward,  but 
also  rotates  it  a  little  on  its  axis  outward. 

The  oblique  muscles  are  superior  and  inferior.  The 
superior  oblique  (Fig.  3,  J)  rises  like  the  recti  at  the 
bottom  of  the  socket,  passes  forward,  contracts  to  a 
slender  tendon,  passes  through  a  loop  situated  in.  the 
forward  part  of  the  socket,  on  the  inner  (nasal)  and  up- 
per side  (Fig.  3,  c) ;  it  then  turns  upon  itself  backward 
and  outward,  passes  over  the  globe  obliquely  across 
the  equator,  and  is  attached  to  the  sclerotic,  or  white 
coat  of  the  eye,  on  the  outside,  a  little  behind  the 
equator.  From  its  last  direction  it  is  evident  that  its 
function  is  to  turn  the  eye  outward  and  downward, 
and  at  the  same  time  to  rotate  it  on  its  axis  inward,  i.  e., 
sinistrally  for  the  right  eye  and  dextrally  for  the  left. 
The  inferior  oblique  (Fig.  3,  d)  rises  from  the  anterior, 
inner,  and  lower  portion  of  the  socket,  passes  outward 
and  backward  beneath  the  ball,  and,  crossing  the  equator 
obliquely,  is  attached  to  the  ball  on  the  outside,  a  little 
behind  the  equator.  From  its  direction  it  is  evident 
that  its  function  is  to  turn  the  eye  inward  and  upward, 
and  at  the  same  time  to  rotate  it  on  its  axis  outward, 
i.  e.,  dextrally — or  like  the  hands  of  a  watch — for  the 
right  and  sinistrally  for  the  left. 

Illustrations  of  these  Actions. — If  we  desire  to  look 
upward,  we  bring  into  action  the  two  superior  recti; 
if  downward,  the  two  inferior  recti ;  if  to  the  right,  the 
exterior  rectus  of  the  right  and  the  interior  rectus  of 
the  left  eye ;  if  to  the  left,  the  external  rectus  of  the 
left  and  internal  of  the  right.  If  we  desire  to  look  at 


20  MONOCULAR  VISION. 

a  very  near  object,  as,  for  example,  the  root  of  the  nose, 
then  the  two  interior  recti  are  brought  into  action.  But 
we  can  not  voluntarily  bring  into  action  the  two  exterior 
recti  to  turn  the  eyes  outward,  nor  the  superior  rectus 
of  one  eye  and  \k&  inferior  Tectus  of  the  other,  so  as  to 
turn  the  one  eye  upward  and  the  other  downward. 
The  reason  of  this  is  because  such  motions,  so  far  from 
subserving  any  useful  purpose,  would  only  confuse  us 
with  double  images,  as  will  be  explained  hereafter,  and 
therefore  have  never  been  learned. 

Malpositions  of  the  eye,  such  as  squinting,  are  the 
result  of  too  great  contraction  of  one  of  the  recti  mus- 
cles, usually  the  internal.  It  is  often  cured  by  cutting 
the  muscle,  and  allowing  it  to  attach  itself  to  a  new  point. 

The  Eyeball. — We  have  thus  far  spoken  only  of  what 
is  external  to  the  ball,  viz.,  the  socket,  the  muscles,  etc. 
We  come  now  to  explain  the  structure  of  the  ball  itself. 
Suppose,  then,  the  ball  be  removed  from  the  socket, 
and  the  muscles  and  connective  tissue  be  dissected 
away;  let  us  examine  more  minutely  its  form  and 
structure. 

The  eye  thus  separated  is  nearly  a  perfect  globe, 
except  that  the  front  part  is  more  protuberant  (Fig.  4). 

1.  The  outer  investing  coat,  except  the  small  pro- 
tuberant front  part,  is  a  strong,  thick,  fibrous  membrane 
of  a  porcelain-white  color,  called  the  sclerotic.     This 
is  partly  exposed  in  the  living  eye,  and  is  called  the 
"  white  of  the  eye."     By  its  strength,  toughness,  and 
elasticity  it  gives  form  without  rigidity.     On  this  ac- 
count the  ball  yields  to  pressure,  but  quickly  regains 
its  form.     It  also  serves  as  the  basis  of  attachment  for 
the  muscles.      If  we  compare  the  eye  to  a  globular 
watch,  then  the  sclerotic  represents  the  outer  case. 

2.  The  more  protuberant  part  of  the  ball  is  covered 


GENERAL  STRUCTURE   OF  THE  EYE.  21 

with  a  thick,  strong,  but  very  transparent  membrane, 
called  the  cornea  ((7,  Fig.  4).  It  corresponds  to  the 
crystal  of  the  watch.  Its  function  is  to  admit  the  light, 
and  at  the  same  time  to  refract  it,  so  as  to  assist  in  form- 
ing the  image,  as  will  be  explained  hereafter. 

FIG.  4. 


SECTION  OF  Tire  EYE.— 0,  optic  nerve;  S. sclerotic ;  Ch,  choroid ;  R, retina;  v,  vitre- 
ous body ;  (7m,  ciliary  muscle ;  Cj,  conjunctiva ;  C,  cornea ;  /,  iris ;  Z,  lens ; 
*,  aqueous  humor ;  **,  ciliary  body  or  zonule  of  Zinn. 

3.  Running  across  from  the  circle  of  junction  of 
the  cornea  with  the  sclerotic,  and  thus  cutting  off  the 
more  protuberant  clear  part  from  the  main  part  of  the 
ball,  and  thus  corresponding  in  position  to  the  face  of 
the  watch,  there  is  an  opaque,  colored  plate  called  the 
iris,  I.  It  is  the  colored  part  of  the  eye,  black,  brown, 
blue,  or  gray,  in  different  individuals.  This  transverse 
plate  is  not  perfectly  flat,  but  protrudes  a  little  in  the 
middle.  In  its  center  is  a  round  hole,  called  the  pupil. 


22  MONOCULAR  VISION. 

corresponding  in  position  with  the  hole  in  the  watch 
face  for  attachment  of  the  hands.  The  pupil  seems  to 
be  jet  black,  because  the  observer  looks  through  the 
pupil  into  the  dark  interior  of  the  ball.  The  function 
of  the  pupil  is  to  admit,  and  at  the  same  time  regulate 
the  amount  of,  light. 

4.  Linings. — Thus  much  is  visible  to  the  naked  eye 
without  dissection.  But,  if  the  ball  be  now  carefully 
opened,  the  part  behind  the  iris  is  found  to  be  lined 
with  two  thin  membranes,  (a.)  Immediately  in  con- 
tact with  the  sclerotic  is  the  choroid,  a  thin  membrane, 
the  cells  of  which  are  colored  with  black  pigment,  which 
gives  it  a  deep-brown,  velvety  appearance.  Its  function 
is  to  quench  the  light  as  soon  as  it  has  done  its  work 
of  impressing  the  retina.  The  anterior  portion  of  the 
choroid,  separated  from  the  sclerotic,  drawn  together 
as  a  curtain,  and  thickened  by  muscular  tissue,  forms 
the  iris  already  described.  Just  before  separating  from 
the  sclerotic  to  form  the  iris,  it  splits  into  two  layers : 
one,  the  anterior,  goes  to  form  the  iris,  as  already  said, 
while  the  other,  the  posterior,  is  gathered  into  a  circular, 
plaited  curtain,  or  series  of  converging  folds,  which 
surrounds  the  outer  margin  of  the  lens  (to  be  pres- 
ently described)  like  a  dark,  plaited  collar.  These  plaits, 
or  folds,  seventy  to  seventy-two  in  number,  are  called 
the  ciliary  processes  (Fig.  5,  and  <?,  Fig.  19,  p.  43).  Be- 
neath this  dark,  plaited  collar,  and  therefore  in  contact 
with  the  sclerotic,  is  a  muscular  collar,  with  radiating 
fibers,  called  the  ciliary  muscle.  (J.)  Within  the  choroid, 
innermost  and  most  important  of  all,  is  the  retina.  This 
is,  in  fact,  a  concave  expansion  of  the  optic  nerve  (0, 
Fig.  4).  This  nerve,  coming  from  the  brain,  enters  the 
eye-socket  near  its  point,  penetrates  the  sclerotic  and 
the  choroid,  then  spreads  out  within  as  a  thin,  concave 


GENERAL  STRUCTURE  OF  THE  EYE.  23 

membrane  of  nerve-tissue,  covering  the  whole  interior 
of  the  ball  as  far  forward  as  the  ciliary  collar.  Its 
function  is  to  receive  and  respond  to  the  impressions 
of  light.  Its  wonderful  structure  and  functions  will  be 
explained  hereafter. 

5.  Contents. — The  ball  thus  described  is  not  hollow 
and  empty,  but  filled  with 
refractive  media,  as  transpa- 
rent as  finest  glass.      These 
are : 

(a.)  Crystalline,  or  Lens. 
— Immediately  behind  the 
iris,  and  in  contact  with  it, 
is  found  the  crystalline.  It 
is  a  flattened  ellipsoid,  or 
double  convex  leas,  as  clear 
as  finest  glass,  about  one 
third  of  an  inch  in  diameter, 
and  one  sixth  of  an  inch  in  SECTI°*  OF  EYE.-«,  sclerotic ;  &,  cor- 

nea;  c,  conjunctiva;  <?,  iris ;«,  lens ; 

thlCKneSS,      firm      enOUgh      tO        /  ciliary  muscle  behind  the  dark 
handle  easily,  but  elastic   and         ciliary  processes ;  g  retina;  h,  optic 
»'  nerve.    (After  Cleland.) 

easily   yielding   to    pressure. 

On  section  it  is  found  to  consist  of  layers,  increasing  in 
density  from  surface  to  center,  as  shown  in  Fig.  5,  e, 
and  in  Fig.  13,  on  page  37.  The  lens  is  invested  with 
a  very  thin,  transparent  membrane,  capsule  of  the  lens, 
which  not  only  invests  it,  but  continues  outward  as  a 
plaited  curtain,  to  be  attached  to  the  sclerotic  near  the 
junction  of  the  cornea.  The  elastic  rigidity  of  the 
sclerotic  pulls  gently  on  this  curtain  and  makes  it  taut, 
and  the  taut  membrane  in  its  turn  presses  gently  on 
the  elastic  compressible  crystalline  and  slightly  flattens 
it.  We  shall  see  the  importance  of  this  when  we  come 
to  speak  of  the  adjustment  of  the  eye  for  distance. 
2 


24:  MONOCULAR  VISION. 

The  perfect  transparency  of  the  lens  is  obviously 
necessary  for  distinct  vision ;  cataract,  a  common  cause 
of  blindness,  arises  from  its  opacity. 

The  lens,  with  its  continuing  curtain,  completely 
divides  the  interior  of  the  ball  into  two  compartments, 
an  anterior  and  a  posterior. 

(J.)  The  anterior  chamber  is  filled  with  a  clear, 
aqueous  liquor,  called  the  aqueous  humor  (Figs.  4  and 
5),  a  small  portion  of  which  is  behind  the  iris,  but  by 
far  the  larger  portion  between  the  iris  and  the  cornea. 
The  two  parts  are  in  connection  through  the  pupil.  If 
the  cornea  be  punctured,  the  aqueous  humor  runs  out, 
the  clear  protuberant  part  of  the  eye  collapses,  and  the 
sight  is  for  the  time  ruined.  If,  however,  the  wound 
heals  without  scar,  or  if  the  scar  be  to  one  side  of  the 
direct  line  of  sight,  the  cornea  will  fill  again  and  the 
sight  may  be  recovered. 

(0.)  The  posterior  and  much  larger  chamber  is  filled 
with  a  transparent,  glassy  substance,  about  the  consist- 
ence of  soft  jelly,  called  the  vitreous  humor.  This 
humor  is  in  direct  contact  with  the  lens  and  curtain  in 
front,  and  with  the  retina  over  its  whole  globular  sur- 
face. 


SECTION  II.— FORMATION  OF  THE  IMAGE. 

The  eyeball,  as  thus  described,  may  be  regarded  as 
consisting  essentially  of  two  distinct  portions,  viz.:  1. 
A  nervous  expansion,  the  retina,  specialized  for  respond- 
ing to  light -vibrations;  2.  An  optical  instrument,  the 
lens  apparatus,  placed  in  front  of  the  retina,  and  spe- 
cially arranged  to  make  the  impression  of  light  strong 
and  definite,  by  means  of  an  image.  These  two  are 


FORMATION   OF  THE   IMAGE.  25 

entirely  different  in  their  origin.  In  embryonic  devel- 
opment, the  one  is  an  outgrowth  from  the  brain,  the 
other  an  ingrowth  from  the  epidermis  and  cutaneous 
tissues.  These  afterward  meet  and  unite  to  form  this 
wonderful  organ. 

Now  the  sole  object  of  this  complex  instrument  is 
the  formation  of  a  perfect  image  on  the  retina.  With- 
out images  we  would  perceive  light,  but  not  objects ; 
and  distinctness  of  objects  is  exactly  proportioned  to 
distinctness  of  retinal  images.  If  the  image  of  an  ob- 
ject is  distinct,  the  object  will  be  distinct ;  if  the  image 
is  blurred,  the  object,  both  in  outline  and  in  details  of 
surface,  will  be  blurred.  If  there  is  no  image,  no  object 
will  be  visible.  Therefore  the  image  must  be  a  fac- 
simile of  the  real  object,  for  the  apparent  object  wiU 
he  a  fac-simile  of  the  image. 

Conditions  of  a  Perfect  Image. — A  serviceable  image 
must  be  sufficiently  bright,  and  perfectly  sharp  and  dis- 
tinct in  outline.  Brightness  only  requires  a  sufficient 
amount  of  light.  In  order  to  be  perfectly  distinct,  it 
is  necessary  that  rays  from  different  points  in  the  object, 
even  the  most  contiguous,  should  not  mix  on  the  image, 
but  all  the  rays  from  each  point  on  the  object  must  be 
carried  to  its  own  point  on  the  image.  Now,  it  is  im- 
possible that  both  of  these  conditions  should  be  fulfilled, 
except  by  some  such  arrangement  as  we  find  in  the 
eye. 

For  see  :  suppose  the  light  to  enter  by  a  hole  only, 
like  the  pupil ;  and,  further,  in  order  that  there  be  light 
enough,  let  the  hole  be  somewhat  large  ;  then  the  light, 
diverging  from  any  point,  5,  Fig.  6,  A,  of  the  object  a  b  c, 
and  entering  the  hole  h  of  diaphragm  d  d,  will  form  a 
diverging  pencil,  and  spread  out  over  the  whole  circle 
J',  on  the  screen  s  s.  Similarly,  the  rays  from  a  will 


26  MONOCULAR  VISION. 

spread  out  and  form  the  circle  a\  and  from  c  the  circle 
c' .  Thus  it  is  seen  that  rays  from  widely  different 
points  in  the  object  mix  with  each  other  on  the  receiv- 
ing screen ;  much  more,  then,  would  rays  from  contigu- 
ous points  of  the  object  mix.  In  such  a  case,  the  mixing 
is  so  great  that  no  recognizable  image  is  formed  at  all. 


FIG.  6. 


As  the  hole  becomes  smaller,  the  circles  of  dispersion, 
a!  1}'  c',  become  smaller  in  the  same  proportion ;  and, 
therefore,  the  light  from  different  points  of  the  object 
is  more  and  more  separated  on  the  receiving  screen, 
and  the  image  becomes  first  recognizable,  then  more 
and  more  distinct.  But,  in  the  mean  time,  the  quantity 
of  light  is  becoming  less  and  less,  and  therefore  the 
image  fainter  and  fainter.  If  we  suppose  the  hole  to 
become  a  mathematical  point,  then  one  ray  only  passes 
from  each  point  to  the  object,  and  goes  to  its  own  place 
in  the  image  (Fig.  6,  J5),  and  the  conditions  of  distinct- 
ness are  fulfilled ;  but  the  image  is  now  infinitely  faint, 
and  therefore  invisible.  If,  now,  we  try  to  increase  the 
brightness  by  increasing  the  size  of  the  hole,  in  propor- 


FORMATION  OF  THE  IMAGE.  27 

tion  as  we  get  brightness  do  we  lose  distinctness.  We 
can  not  get  both  at  the  same  time. 

Experiment.— Let  a  room  with  solid  shutters  be  dark- 
ened ;  let  one  shutter  have  a  hole  of  a  few  inches  in 
diameter ;  cover  the  hole  with  an  opaque  plate  of  sheet 
iron,  in  which  there  is  a  very  small  hole,  one  tenth  to 
one  twentieth  of  an  inch  in  diameter.  If,  now,  a  sheet 
of  white  paper  be  held  a  little  way  from  the  small  hole, 
an  inverted  image  of  the  external  landscape  will  be  seen 
on  the  sheet.  If  we  increase  the  size  of  the  hole,  the 
image  will  be  brighter,  but  also  more  blurred. 

Illustrations. — Many  simple  experiments  may  be 
made  illustrating  this  principle.  A  pinhole  in  a  card 
will  make  an  inverted  image  of  a  candle  flame.  When 
the  sun  is  in  eclipse,  it  may  be  examined  without  smoked 
glass,  by  simply  allowing  it  to  shine  through  a  pinhole 
in  a  card  upon  a  suitable  screen.  In  the  shade  of  a  very 
thick  tree-top  the  sun-flecks  are  circular  like  the  sun ; 
but  during  an  eclipse  they  are  crescentic,  or  even  annu- 
lar, according  to  the  degree  of  obscuration.  They  are 
always  images  of  the  sun. 

Property  of  a  Lens. — Now  a  lens  has  the  remarkable 
property  of  accomplishing  both  these  apparently  oppo- 

FIG.  7. 


site  ends,  viz.,  brightness  and  distinctness  at  the  same 
time.  If  an  object,  a  c,  be  placed  before  a  lens,  L  (Fig. 
7),  then  all  the  rays  diverging  from  any  point,  J,  are 


28  MONOCULAR  VISION. 

bent  so  as  to  come  together  again  at  the  point  bf.  Of 
the  divergent  pencil,  I  L  L,  the  central  ray  passes 
straight  through  without  deviation ;  rays  a  little  way 
from  the  central  are  bent  a  little ;  rays  farther  away 
are  bent  more  and  more  according  to  their  angle  of 
divergence,  so  that  they  all  meet  at  the  same  point,  bf. 
Similarly  all  the  rays  proceeding  from  a,  and  falling  on 
the  lens,  are  brought  to  the  same  point,  a',  and  from  c 
to  the  point  c',  and1  so  also  for  every  intermediate  point. 
Thus  an  image  is  formed  which  is  both  bright  and  very 
distinct  if  the  receiving  screen  is  suitably  placed,  i.  e., 
at  the  exact  place  where  the  rays  meet.  The  billions 
of  rays  from  millions  of  points  of  the  surface  of  the 
object  are,  as  it  were,  sifted  out  by  the  law  of  refraction, 
and  each  safely  conveyed  to  its  own  point  in  the  image  ; 
so  that,  for  every  radiant  point  of  the  object,  there  is  a 
corresponding  focal  point  in  the  image.  But  it  is  evi- 
dent that  the  screen  must  be  suitably  placed,  for,  if  it 
be  placed  too  near,  at  #'  $',  the  rays  have  not  yet  come 
together ;  if  too  far,  at  Sff  /$",  the  rays  have  already  met, 
crossed,  and  again  diverged.  In  both  cases  the  image 
will  be  blurred. 

FIG.  8. 


DIAGRAM  ILLUSTRATING  THE  FORMATION  OF  AN  IMAGE  CN  HIE  RETINA. 

In  all  dioptric  instruments  images  are  formed  in  this 
way.  It  is  in  this  way  that  images  are  formed  in  the 
eye.  In  Fig.  8  it  is  seen  that  the  diverging  pencils, 


FORMATION  OF  THE   IMAGE.  29 

from  points  A  and  B  of  the  object,  which  enter  the 
pupil,  are  refracted  by  the  lenses  of  the  eye,  and  brought 
to  a  focus  on  the  retinal  screen  at  of  b'.  Now,  since 
the  rays  from  every  intermediate  point  of  the  object 
will  be  similarly  focused,  we  will  have  a  perfect  image 
of  the  object  painted  on  the  retina. 

This  fundamental  fact  may  be  proved  in  many 
ways  by  observations  on  the  dead  eye :  1.  If  the  eye 
of  an  ox  be  taken  from  the  socket,  and  the  sclerotic 
carefully  removed,  so  that  the  back  parts  of  the  eye  are 
somewhat  transparent,  a  miniature  image  of  the  land- 
scape may  be  seen  there ;  or,  2.  If  we  remove  the  eye- 
ball of  a  white  rabbit,  we  will  find  that,  on  account  of 
the  absence  of  black  pigment  in  the  choroid  of  these 
albinos,  the  transparency  of  the  coats  of  the  eye  enables 
us  to  see  the  image,  even  through  the  sclerotic,  or  much 
more  distinctly  if  the  sclerotic  be  removed ;  or,  3.  We 
may  remove  all  the  coats  of  the  dead  eye  and  replace 
them  by  a  film  of  mica — the  image  will  be  very  dis- 
tinct ;  or,  4.  The  image  may  be  seen  in  the  living  eye 
by  means  of  the  ophthalmoscope. 

By  reference  to  the  diagram,  Fig.  8,  it  is  seen  that 
the  central  rays  from  all  radiants  cross  each  other  in 
the  lens.  This  point  of  ray-crossing  is  called  the  nodal 
point.  It  is  a  little  behind  the  center  of  the  lens. 


CHAPTER  II. 

THE  EYE  AS  AN  OPTICAL  INSTRUMENT. 

THE  further  explanation  of  the  wonderful  mechanism 
of  the  eye  is  best  brought  out  by  a  comparison  with  some 
optical  instrument.  We  select  for  this  purpose  the 
photographic  camera.  The  eye  and  the  camera:  the 
one  a  masterpiece  of  Nature's,  the  other  of  human 
art. 

We  pass  over,  with  bare  mention,  some  obvious  re- 
semblances, in  which,  however,  the  superiority  of  the 
eye  is  evident :  such,  e.  g.,  as  the  admirable  arrange- 
ment of  the  lids  for  wiping  and  keeping  bright  while 
using,  and  for  covering  when  not  in  use ;  also,  the  ad- 
mirable arrangement  of  muscles,  by  which  the  eye  is 
turned  with  the  greatest  rapidity  and  precision  on  the 
object  to  be  imaged,  so  superior  to  the  cumbrous  move- 
ment of  the  camera  for  the  same  purpose.  We  pass 
over  these  and  many  other  minor  points  to  come  at 
once  to  the  main  points  of  comparison. 

Take,  then,  the  eye  out  of  the  socket — the  dead  eye — 
and  the  camera  without  its  sensitive  plate — with  only  the 
insensitive  ground-glass  receiving  plate.  They  are  both 
now  pure  optical  instruments,  and  nothing  more.  They 
are  both  contrived  for  the  same  purpose,  viz.,  the  for- 
mation of  a  perfect  image  on  a  screen  properly  placed. 


THE  EYE  AS  AN  OPTICAL  INSTRUMENT.  31 

Look  into  the  camera  from  behind,  and  we  see  the 
inverted  image  on  the  ground-glass  plate  ;  look  into  the 
eye  from  behind,  and  we  see  also  an  inverted  image  on 
the  retina.  The  end,  therefore,  is  the  same  in  the  two 
cases.  We  now  proceed  to  show  that  the  means  by 
which  the  end  is  attained  are  also  similar. 

1.  The  camera  is  a  small,  dark  chamber,  open  to 
light  only  in  front,  to  admit  the  light  from  the  object  to 
be  imaged.     It  is  coated  inside  with  lampblack,  so  that 
any  light  from  the  object  to  be  imaged  or  from  other 
objects  which  may  fall  on  the  sides  will  be  quenched, 
and  not  allowed  to  rebound  by  reflection,  and  thus  fall 
on  the  image  and  spoil  it.     No  light  must  fall  on  the 
image  except  that  which  comes  directly  from  the  object. 
So  the  eye  also  is  a  very  small,  dark  chamber,  open  to 
light  only  in  front,  where  the  light  must  enter  from  the 
object  to  bo  imaged,  and  lined  with  dark  pigment,  to 
quench  the  light  as  soon  as  it  has  done  its  work  of  im- 
pressing its  own  point  of  the  retina,  and  thus  prevent 
reflection  and  striking  some  other  part,  and  thus  spoil- 
ing the  image. 

2.  Both  camera  and  eye  form  their  images  by  means 
of  a  lens  or  a  system  of  lenses.     The  manner  in  which 
these  act  in  forming  an  image  has  already  been  ex- 
plained (page  28).    It  is  precisely  the  same  in  both  cases. 
But  lenses  which  form  a  perfect  image  are  very  difficult 
of  construction.     There  are,  especially,  two  main  im- 
perfections which  must  be  corrected,  viz.,  chromatism 
and  aberration. 

3.  Correction  of  Chromatism. — In  the  image  formed 
by  a  simple,  ordinary  lens,  all  the  outlines  of  figures  are 
found  to  be  slightly  edged  with  rainbow  hues.     If  we 
look  through  such  a  lens  at  an  object,  the  outlines  of 
the  object  will  be  similarly  edged  with  colors,  especially 


32  MONOCULAR  VISION. 

if  the  object  lie  near  the  margin  of  the  field  of  the 
lens.     This  is  explained  as  follows  : 

Ordinary  sunlight,  as  every  one  knows,  consists  of 
many  colors  mixed  together,  the  mixture  producing  the 
impression  of  white.  If  a  beam  of  sunlight  be  made  to 
pass  through  a  glass  prism,  the  beam  is  bent :  but  more, 
the  different  colors  are  unequally  bent,  so  that  they  are 
separated  and  spread  out  over  a  considerable  space.  This 
colored  space  is  called  the  spectrum.  In  Fig.  9  the 


FIG.  9. 


r-i\  spectrum  :  r,  red;  o,  orange;  y,  yellow;  g,  green;  6,  blue;  i,  indigo;  «,  violet. 

straight  beam,  a  5,  is  bent  by  the  prism  so  as  to  become 
a  c  d;  this  is  called  refraction.  But  also  the  different 
colors  are  unequally  bent ;  red  is  bent  least  and  violet 
most,  the  other  colors  lying  between  these  extremes ; 
thus  they  are  spread  out  over  a  considerable  colored 
space.  This  unequal  refraction  is  called  dispersion. 
If  we  look  through  a  prism  at  objects,  we  will  find  that 
the  outlines  of  the  objects  will  be  edged  with  exactly 
similar  colors.  JSTow  all  refraction  is  accompanied  by 
dispersion ;  therefore  a  simple,  uncorrected  lens  always 
disperses,  especially  on  the  edges  where  the  refraction  is 
greatest ;  and,  therefore,  also,  the  images  made  by  such 
a  lens  will  be  edged  with  color.  Thus  the  light  from 
the  radiant  a  (Fig.  10),  being  white  light,  is  dispersed  ; 
the  violet  rays,  being  more  bent,  reach  a  focus  at  a \ 


THE   EYE  AS  AN  OPTICAL  INSTRUMENT. 


33 


but  the  red  only  at  a",  the  other  colors  at  intermediate 
points.  There  is,  therefore,  no  place  where  all  the 
rays  from  the  radiant  come  to  a  focus — there  is  no 
common  focal  point  for  the  radiant  a.  The  best  pla£e 


FIG.  10. 


FIG.  11. 


for  the  receiving  screen  would  be  8  8,  but  even  here 
there  is  no  perfect  focus.  Evidently,  therefore,  the 
conditions  of  a  perfect  image  are  not  fulfilled.  This 
defect  must  be  corrected.  It  is  corrected  in  every  good 
lens. 

In  order  to  understand  how  this  is  done,  it  must  be 
remembered,  first,  that  concave  and  convex  lenses  an- 
tagonize, and,  if  of  equal  refractive  power,  neutralize 
each  other.  Therefore,  a  combination  of  a  double  con- 
vex and  a  double  concave  lens,  if  of  same  material  and 
of  equal  curvature,  like  Fig.  11, 
A,  will  produce  no  refraction,  be- 
cause the  refraction  produced  in 
one  direction  by  the  convex  lens 
is  completely  destroyed  by  refrac- 
tion in  the  opposite  direction  by 
the  concave  lens.  Such  a  com- 
bination will  therefore  make  no 
image.  In  order  that  such  a  combination  should  make 
an  image  at  all,  it  is  necessary  that  the  convexity  should 
predominate  over  the  concavity,  as  in  Fig.  11,  B. 
Again,  it  must  be  remembered  that  dispersion  is  not 
always  in  proportion  to  refraction.  Some  substances 


34  MONOCULAR   VISION. 

have  a  higher  refractive  power  and  a  comparatively 
low  dispersive  power,  and  vice  versa.  This  is  the  case 
with  different  kinds  of  glass. 

Now,  suppose  we  select  a  glass  with  excess  of  refrac- 
tive over  dispersive  power  for  our  convex  lens,  and  one 
with  excess  of  dispersive  over  refractive  power  for  our 
plano-concave  lens  (Fig.  11,  B\  and  cement  these  to- 
gether as  a  compound  lens :  it  is  evident  that  these  may 
be  so  related  that  the  plano-concave  lens  shall  entirely 
correct  the  dispersion  of  the  convex  lens  without  neu- 
tralizing its  refraction,  and  therefore  the  combination 
will  be  a  refractive,  but  not  a  dispersive,  lens,  and  there- 
fore will  make  an  image  without  colored  edges.  Such 
a  compound  lens  is  called  achromatic. 

This  is  the  way  in  which  art  makes  achromatic 
lenses,  and  all  good  optical  instruments  have  lenses  thus 
corrected.  Now,  the  lenses  of  the  eye  are  apparently 
corrected  in  a  similar  manner.  The  eye  consists  of 
three  lenses — the  aqueous,  the  crystalline,  and  the  vit- 
reous. These  have  curvatures  of  different  kinds  and 
degrees :  the  aqueous  lens  is  convex  in  front  and  con- 
cave behind ;  the  crystalline  is  bi-convex ;  the  vitreous 
is  concave  in  front.  As  its  convex  outer  surface  can  not 
be  regarded  as  a  refracting  surface,  since  this  is  in  direct 
contact  with  the  screen  to  be  impressed,  it  may  be  con- 
sidered as  a  plano-concave  lens.  The  refractive  powers 
of  the  material  of  these  are  also  different :  that  of  the 
crystalline  being  greatest,  and  the  aqueous  least*  The 
dispersive  powers  of  these  have  not  been  determined, 
but  they  probably  differ  in  this  respect  also.  Thus, 
then,  we  have  here  also  a  combination  of  different 
lenses,  of  different  curvatures,  and  different  refractive, 
and  probably  dispersive,  power,  and  for  the  same  pur- 
pose, viz.,  correction  of  chromatism.  It  is  an  interest- 


THE  EYE  AS  AN  OPTICAL   INSTRUMENT.  35 

ing  historic  fact  that  the  hint  for  correction  of  chro- 
matism  by  combination  of  lenses  was  taken  from  the 
structure  of  the  eye  by  Euler,  and  afterward  carried  out 
successfully  by  Dollond.  That  the  chromatism  of  the 
eye  is  substantially  corrected  is  shown  by  the  complete 
absence  of  colored  edges  of  strongly  illuminated  objects, 
and  the  sharp  definition  of  objects  seen  by  good  eyes. 
By  close  observation  and  refined  methods,  it  has  been 
recently  shown  that  the  chromatism  of  the  eye  is  not 
perfectly  corrected.  It  can  be  observed  if  we  use  only 
the  extreme  colors,  red  and  violet.*  But  the  degree  of 
chromatism  is  so  small  as  not  to  interfere  at  all  with 
the  accuracy  of  vision. 

4.  Aberration. — Another  defect,  much  more  diffi- 
cult to  correct,  is  aberration.  The  form  of  lens  most 
easily  made  has  a  spherical  curvature.  But  in  such  a 
lens  there  is  an  excess  of  refractive  power  in  the  'mar- 
ginal portions  as  compared  with  the  central  portions ; 
an  excess  increasing  with  the  distance  from  the  center ; 
therefore  the  focal  point  for  marginal  rays  is  not  the 

FIG.  12. 


same  as  for  the  central  rays,  but  nearer.  In  Fig.  12 
the  marginal  rays,  a  r ',  a  r',  are  brought  to  a  focus  at 
a",  while  the  central  rays,  a  r,  a  r,  are  brought  to  a 
focus  at  a'.  The  best  place  for  the  receiving  screen 
would  be  at  S  8,  between  these ;  but  even  there  the 
image  would  not  be  sharp.  In  such  a  lens  there  is  no 

*  Helmholtz,  "  Popular  Lsctures,"  p.  216. 


36  MONOCULAR  VISION. 

common  focal  point  for  all  the  rays,  and  therefore  the 
conditions  of  perfect  image  are  not  fulfilled — the  image 
is  blurred.  This  defect  must  be  corrected.  It  is  cor- 
rected in  the  best  lenses. 

The  aberration  may  be  greatly  decreased  by  the  use 
of  diaphragms,  which  cut  off  all  but  the  central  rays ; 
but  in  this  case  we  get  distinctness  at  the  expense  of 
brightness.  This  may  be  done  when  the  light  is  very 
intense.  Again,  the  aberration  may  be  reduced  by 
using  several  very  flat  lenses,  instead  of  one  thick  lens. 
This  plan  is  used  in  many  instruments.  But  complete 
correction  can  only  be  made  by  increasing  the  refraction 
of  the  central  portions  of  the  lens,  and  this  may  con- 
ceivably be  accomplished  in  two  ways,  viz.,  either  by 
increasing  the  curvature  of  this  part  or  by  increasing 
its  density,  and  therefore  its  refractive  index.  It  is  by 
the  former  method  that  art  makes  the  correction.  By 
mathematical  calculation,  it  is  found  that  the  curve  must 
be  that  of  an  ellipse.  A  lens,  to  make  a  perfect  image, 
must  not  be  a  segment  of  a  sphere,  but  of  the  end  of 
an  ellipsoid  of  revolution  about  its  major  axis.  It  is 
justly  considered  one  of  the  greatest  triumphs  of  science 
to  have  calculated  the  curve,  and  of  art  to  have  carried 
out  with  success  the  suggestion  of  science. 

Art  has  not  been  able  to  achieve  success  by  the 
second  method.  It  is  impossible  so  to  graduate  the  in- 
creasing density  of  glass  from  the  surface  to  the  center 
of  a  lens  as  to  correct  aberration.  Now,  it  is  apparently 
this  second  method,  or  perhaps  both,  which  has  been 
adopted  by  nature.  The  crystalline  lens  increases  in 
density  and  refractive  power  from  surface  to  center,  so 
that  it  may  be  regarded  as  consisting  of  ideal  concentric 
layers,  increasing  in  density  and  curvature  until  the 
central  nucleus  is  a  very  dense  and  highly  refractive 


THE   EYE   AS  AN  OPTICAL   INSTRUMENT.  37 

spherule  (Fig.  13).  The  surface  of  the  cornea  has  the 
form  of  an  ellipsoid  of  revolution  about  its  major  axis, 
and  therefore  doubtless  contributes  to  the  same  effect. 
In  looking  at  very  near  objects,  the  con- 
traction of  the  pupil,  also,  by  cutting  off 
marginal  rays,  tends  in  the  same  direc- 
tion. However  the  result  may  be  ac- 
complished, whether  by  one  or  by  both 
methods,  it  is  certain  that  in  good  eyes 
it  is  completely  achieved,  for  the  clear-  SECTION  ~OW1HO  TIIE 
ness  of  vision  is  wholly  conditioned  on  STRUCTURE  OF  THB 
the  sharpness  of  the  retinal  image. 

It  is  probable  that  the  peculiar  structure  of  the  crys- 
talline lens  described  above  has  also  another  important 
use  in  the  lower  animals,  if  not  in  man.  Dr.  Ludi- 
mar  Hermann  *  has  shown  that,  in  a  homogeneous 
lens,  while  the  rays  from  radiants  near  the  middle  of 
the  field  of  view,  i.  e.,  nearly  directly  in  front,  are 
brought  to  a  perfect  focus,  the  rays  from  radiants  situ- 
ated near  the  margins  of  the  field  of  view,  i.  e.,  of  very 
oblique  pencils,  are  not  brought  to  a  focus.  Therefore 
the  picture  formed  by  such  a  lens  is  distinct  in  the  cen- 
tral parts,  but  very  indistinct  on  the  margins.  Now, 
this  defect  of  a  homogeneous  lens,  Dr.  Hermann  shows, 
is  entirely  corrected  by  the  peculiar  structure  of  the 
crystalline ;  therefore  this  structure  confers  on  the  eye 
the  capacity  of  seeing  distinctly  over  a  wide  field,  with- 
out changing  the  position  of  the  point  of  sight.  This 
capacity  he  calls  periscopism.  We  will  hereafter,  how- 
ever, give  reasons  showing  that  this  property  of  the 
crystalline  can  be  of  little  value  to  man. 

5.  Adjustment  for  Light. — The  delicate  work  done 
by  the  camera  and  by  the  eye  requires  a  proper  regulation 

*  "Archives  des  Sciences,"  vol.  kiii,  p.  66.     18*75. 


38 


MONOCULAR  VISION. 


of  the  amount  of  light.  In  both,  therefore,  we  want 
some  contrivance  by  which,  when  the  light  is  very  in- 
tense, a  large  portion  may  be  shut  out,  and  when  the 
light  is  feeble,  a  larger  portion  may  be  admitted.  In 
optical  instruments  this  is  done  by  means  of  diaphragms. 
In  the  camera  we  have  brass  caps  with  holes  of  various 
sizes,  which  may  be  changed  and  adapted  to  the  inten- 
sity of  the  light.  In  the  microscope  wTe  have  a  circular 
metallic  plate,  with  holes  of  various  sizes.  By  revolv- 
ing this  plate  we  bring  a  larger  or  a  smaller  hole  in 
front  of  the  lens. 

In  the  eye  the  same  end  is  reached,  in  a  far  more 
perfect  manner,  by  means  of  the  iris.     The  iris  (Fig. 

PIG.  14. 


FIG.  15. 


HITMAN  EYE,  ENLARGED,  WITH  PART  OF  CORNEA  AND 
SCLEROTIC  REMOVED.— a,  sclerotic;  £>,  cornea;  c, 
choroid ;  d,  iris ;  £,  pupil ;  /,  ciliary  muscle.  (Af- 
ter Cleland.) 


SHOWING  STRUCTURE 
OF  IRIS. 


14,  d)  is  an  opaque  circular  disk,  with  a  round  hole, 
the  pupil,  in  the  middle.  The  circumference  of  the 
disk  is  immovably  fixed  to  the  sclerotic  at  its  junction 
with  the  cornea ;  but  the  margin  of  the  circular  hole,  or 
pupil,  is  free  to  move.  The  disk  itself  is  composed  of 
two  sets  of  contractile  fibers,  viz.,  the  radiating  and  the 


THE  EYE  AS  AN  OPTICAL  INSTRUMENT,  39 

circular  (Fig.  15).  The  radiating  fibers  converge  from 
the  outer  margin  of  the  iris  as  a  fixed  point,  and  take 
hold  on  the  movable  margin  of  the  pupil,  and,  when 
they  contract,  pull  opsn  the  pupil  on  every  side,  and 
thus  enlarge  it  (Fig.  15,  B).  The  circular  fibers  are 
concentric  with  the  pupil,  and  are  especially  numerous 
and  strong  near  the  margin,  forming  there  a  band  about 
one-twentieth  of  an  inch  wide.  When  they  contract,  they 
draw  up  the  pupil,  like  a  string  about  the  mouth  01  a  bag, 
and  make  it  small  (Fig.  15,  A).  We  may  regard  the 
radiating  fibers  as  elastic,  and  as  contracting  passively  by 
elasticity  when  stretched ;  and  the  circular  fibers  as  con- 
tracting actively  under  stimulus,  like  a  muscle.  Further, 
the  circular  fibers  are  in  such  sympathetic  relation  with 
the  retina,  that  a  stimulus  of  any  kind,  but  especially 
its  appropriate  stimulus,  light,  applied  to  the  latter, 
causes  the  former  to  contract,  the  extent  of  the  con- 
traction being  of  course  in  proportion  to  the  intensity 
of  the  light.  If,  therefore,  strong  sunlight  impresses 
the  retina,  the  circular  fibers  immediately  contract,  the 
pupil  becomes  small,  and  a  large  portion  of  the  light  is 
shut  out.  When  the  light  diminishes,  as  in  twilight, 
the  circular  fibers  relax,  the  previously  stretched  radi- 
ating fibers  contract  by  elasticity,  and  enlarge  the  pupil. 
At  night  the  pupil  enlarges  still  more,  in  order  to  let 
in  as  much  light  as  possible.  Finally,  if  a  solution  of 
belladonna  (which  completely  paralyzes  the  circular 
fibers)  be  dropped  into  the  eye,  the  pupil  enlarges  so 
that  the  iris  is  reduced  to  a  narrow  dark  ring. 

Art,  taking  the  hint  from  Nature,  and  striving  to 
be  not  outdone,  has  recently  constructed  for  the  micro- 
scope a  diaphragm  somewhat  on  this  plan.  It  is  com- 
posed of  many  very  thin  metallic  plates^  partly  covering 
each  other,  so  arranged  as  to  leave  a  polygonal  hole  in 


40  MONOCULAR  VISION. 

the  middle,  and  sliding  over  each  other  in  such  wise 
that  by  turning  a  milled  head  in  one  direction  they  all 
move  toward  the  central  point  and  dimmish  the  open- 
ing, while  by  turning  in  contrary  direction  they  all 
move  away  from  the  center  and  make  the  hole  larger. 
This  is  confessedly  a  beautiful  contrivance,  but  how 
inferior  to  the  admirable  work  of  Nature  ! 

As  already  stated  (page  37),  contraction  of  the  pupil 
takes  place  not  only  under  the  stimulus  of  light,  but 
also  in  looking  at  very  near  objects.  The  reason  of 
this  is,  that  correction  of  spherical  aberration  is  thus 
made  more  perfect. 

*  6.  Adjustment  for  Distance  —  Focal  Adjustment. 
—We  have  seen  that  a  lens,  properly  corrected  for 
chromatism  and  aberration,  makes  a  perfect  image. 
But  the  plate  or  screen  which  receives  the  image  and 
makes  it  visible  must  be  placed  exactly  in  the  right 
place,  i.  e.,  in  the  focus ;  otherwise  the  image  will  be 
blurred.  We  reproduce  here  (Fig.  16)  the  diagram 

FIG.  16. 


on  page  27,  showing  this.  It  is  at  once  seen  that,  if 
the  receiving  plate  is  too  near  the  lens,  i.  e.,  at ' Sf  8', 
the  rays  from  any  radiant  of  the  object  will  not  yet 
have  come  together  at  a  focal  point.  If  the  receiving 
screen  be  too  far  from  the  lens,  at  S*  Sff,  then  the  rays 
moving  in  straight  lines  will  have  already  met,  crossed, 
and  again  spread  out.  It  is  evident  that  there  is  but  one 


THE  EYE   AS  AN  OPTICAL  INSTRUMENT.  41 

place  where  the  image  is  perfect,  viz.,  at  the  focal 
points,  S  S.  Now,  if  this  place  of  the  image  were  the 
same  for  all  objects  at  all  distances,  it  would  be  only 
necessary  to  find  that  place,  and  fix  the  receiving  plate 
immovably  there.  But  the  place  of  the  image  formed 
by  any  lens  changes  with  every  change  in  the  distance 
of  the  object.  As  the  object  in  front  approaches,  the 
image  on  the  other  side  recedes  from  the  lens.  As  the 
object  recedes,  the  image  approaches  the  lens.  There- 
fore there  must  be  an  adjustment  of  the  instrument  for 
the  distance  of  the  object. 

There  are  only  two  possible  wrays  in  which  this  ad- 
justment can  be  made :  Either  (1st),  the  lens  remaining 
unchanged,  the  screen  must  advance  or  recede  with  the 
image ;  or  (2d),  the  place  of  the  screen  remaining  the 
same,  the  lens  must  be  changed  so  as  always  to  throw 
the  image  on  the  immovable  screen.  The  first  is  the 
mode  of  adjustment  used  in  the  camera,  the  opera-glass, 
the  field-glass,  and  the  telescope;  the  second  is  the 
mode  usually  used  in  the  microscope.  In  the  camera, 
for  example,  when  the  object  comes  nearer,  we  draw 
out  the  tube  so  as  to  carry  the  ground-glass  plate  a  little 
farther  back ;  when  the  object  recedes,  we  slide  up  the 
tube  so  as  to  bring  the  receiving  plate  nearer  the  lens. 
So  in  the  opera-glass  we  elongate  the  tube  for  near  ob- 
jects, and  shorten  it  for  more  distant.  In  the  micro- 
scope, on  the  contrary,  the  image  is  usually  thrown  to 
the  same  place  in  the  upper  part  of  the  tube.  If,  there- 
fore, the  object  approaches  nearer  the  lens  (as  it  does  in 
higher  magnification),  we  change  the  lens  so  as  to  throw 
the  image  to  the  same  place. 

How  is  this  managed  in  the  eye  ?  It  was  long  be- 
lieved that  the  adjustment  was  on  the  plan  of  the 
camera.  Now,  however,  it  is  known  that  it  is  rather  on 


42  MONOCULAR  VISION. 

the  plan  of  the  microscope.  It  was  formerly  thought 
that,  in  looking  at  a  near  object,  the  straight  muscles, 
acting  all  together,  squeezed  the  eye  about  the  equatorial 
belt,  and  increased  its  axial  diameter — in  other  words, 
made  it  egg-shaped — and  thus  carried  the  retinal  screen 
farther  back  from  the  lens.  But  now  it  is  known  that 
the  retinal  screen  remains  immovable,  and  the  lens 
changes  its  form  so  as  to  throw  the  image  to  the  same 
place. 

Experiment. — This  is  proved  in  the  following  man- 
ner :  A  person  is  chosen  with  good,  normal  young  eyes. 
The  experimenter  stands  in  a  dark  room,  in  front  of 

Fia.  IT. 


c(§r 

A,  eye  observed ;  B,  eye  of  observer  ;  c,  section  of  -candle  flame ;  /,  a  distant  point  of 
eight,  and  n  a  near  point  of  sight.    (After  Helmholtz.) 

the  patient,  A,  with  a  lighted  candle  in  his  hand,  a  little 
to  one  side,  as  in  Fig.  17,  <7,  while  his  own  point  of  ob- 
servation is  on  the  other  side,  B.  If  the  observer  now 
looks  carefully,  he  will  see  in  the  eye  of  the  patient 
three  images  of  the  candle-flame  :  first,  one  reflected 
from  the  surface  of  the  cornea,  which  is  by  far  the  bright- 
est (Fig.  18,  a) ;  second,  one  from  the  anterior  surface 
of  the  crystalline,  much  fainter  (Fig.  18,  fy ;  third, 
one  from  the  posterior  surface  of  the  crystalline,  the 
faintest  of  all,  and  very  small  (c).  Further,  it  will  be 
observed  that  the  first  and  second  are  erect  images, 


THE  EYE  AS  AN  OPTICAL  INSTRUMENT. 


43 


FIG.  18. 


because  reflected  from  a  convex  surface,  while  the  third 
is  inverted,  because  reflected  from  a  concave  surface. 
Now  directing  the  patient  to  gaze  on  vacancy,  or  a  dis- 
tant point,  y,  Fig.  17,  we  observe  carefully  the  posi- 
tion and  size  of  these  several  images. 
Then,  if  by  direction  the  patient  trans- 
fers the  point  of  sight  to  a  very  near 
point,  n,  without  changing  the  direc- 
tion, we  observe  that  the  images  a  and 
c  do  not  change,  but  the  image  b  changes 
its  position  and  grows  smaller.  This 
image  is  reflected  from  the  anterior  surface  of  the  crys- 
talline. The  anterior  surface  of  the  crystalline,  there- 
fore, changes  its  form.  Again,  the  nature  of  the  change 
of  the  image,  viz.,  that  it  becomes  smaller,  shows  that  this 
anterior  surface  becomes  more  convex.  By  careful  ex- 
amination the  iris,  too,  may  be  seen  to  protrude  a  little 

FIG.  19. 


F)  lens  adjusted  to _di»4ant  objects ;  W,  to  nejtf  objects ;  a,  aqueous  humor ;  d,  ciliary 
muscle  ;  e,  ciliary  process. 

in  the  middle.  Evidently,  therefore,  in  adjusting  the 
eye  to  very  near  objects,  the  crystalline  becomes  thicker 
in  the  middle,  and  pushes  the  pupil  a  little  forward. 
In  the  accompanying  diagram,  Fig.  19,  the  crystalline 
lens  is  divided  by  a  plane  through  the  center.  The 
right  side,  N,  is  adapted  to  near  objects ;  the  left,  F, 
to  distant  objects, 


44  MONOCULAR   VISION. 

Theory  of  Adjustment — Thus  much  may  be  con- 
sidered certain.  It  is  certain  that  in  adjusting  the  eye 
for  looking  at  very  near  objects,  the  lens  becomes  more 
convex.  But  the  question,  "How  is  this  done?"  is 
more  difficult  to  answer.  Helmholtz  thinks  it  is  done 
in  the  following  manner  :  * 

It  will  be  remembered  that  the  lens  is  invested  by 
a  thin,  transparent  membrane,  which  extends  outward 
from  its  edge  as  a  circular  curtain,  and  is  attached  all 
around  to  the  sclerotic,  thus  dividing  the  interior  of 
the  eye  into  two  chambers — the  anterior,  filled  with  the 
aqueous,  and  the  posterior,  with  the  vitreous  humor.  It 
will  be  remembered,  further,  that  this  membrane  is 
naturally  drawn  tight  by  the  elastic  rigidity  of  the 
sclerotic,  and  presses  gently  on  the  elastic  lens,  flatten- 
ing it  slightly.  This  is  the  normal  passive  condition,  as 
when  gazing  at  a  distance.  Now  there  are  certain 
muscular  fibers  (ciliary  muscle,  Fig.  19,  d)  which,  aris- 
ing from  the  exterior  fixed  border  of  the  iris  just  where 
it  is  attached  to  the  sclerotic,  run  backward,  radiating, 
and  take  hold  upon  the  outer  edge  of  the  lens  curtain. 
When  these  fibers  contract,  they  pull  forward  the  tense 
curtain  to  a  smaller  portion  of  the  globe,  and  thus 
relax  its  tension.  The  relaxing  of  the  tension  of  the 
curtain  relaxes  also  the  pressure  of  the  capsule  on  the 
lens,  which  therefore  immediately  swells  or  thickens  in 
proportion  to  the  degree  of  relaxation.  According  to 
Helmholtz,  then,  we  adjust  the  eye  to  near  objects  by 
contraction  of  the  ciliary  muscle.  There  are  other 
views  on  this  subject,  but  this  seems  the  most  probable. 

The  normal  eye  in  a  passive  state  is  adjusted  to  in- 
finitely distant  objects.  By  change  of  the  form  of  the 
lens,  it  can  adjust  itself  to  all  distances  up  to  about  five 

*  "Optique  Physiologique,"  p.  150. 


THE  EYE  AS  AN   OPTICAL  INSTRUMENT.  45 

inches.  The  range  of  adjustment  or  of  distinct  vision 
is,  therefore,  within  these  limits.  It  is  only  at  compar- 
atively near  distances,  however,  that  the  change  is  great. 
Between  twenty  feet  and  infinite  distance  the  adjust- 
ment is  almost  imperceptible. 

"We  see,  then,  that  the  mode  of  adjustment  of  the 
eye  is  somewhat  like  that  of  the  microscope ;  i.  e.,  the 
change  is  in  the  lens,  not  in  the  position  of  the  receiv- 
ing screen.  Like  the  microscope,  but  how  infinitely 
superior!  The  microscope  has  its  four-inch  lens,  its 
two-inch  lens,  its  one-inch  lens,  its  half-inch  lens,  its 
quarter-inch,  its  tenth-inch,  and  even  its  fiftieth-inch 
lens.  It  changes  one  for  another,  according  to  the  dis- 
tance of  the  object.  But  the  eye  changes  its  one  lens, 
and  makes  it  a  five-inch  lens,  a  foot  lens,  a  twenty-foot 
lens,  a  mile  lens,  or  a  million-mile  lens ;  for  at  all  these 
distances  it  makes  a  perfect  image. 


CHAPTEE  III. 

DEFECTS   OF  THE  EYE  AS  AN  INSTRUMENT. 

IN  the  preceding  chapter  we  have  attempted  to  bring 
out,  in  a  clear  and  intelligible  form,  the  beautiful  struc- 
ture of  the  eye,  by  comparing  it  with  the  camera,  and 
showing  its  superiority.  But  the  eye  of  which  we 
have  been  speaking  is  the  normal  or  perfect  eye.  This 
normal  condition  is  called  emmetropy.  The  eye,  how- 
ever, is  not  always  a  perfect  instrument.  There  are 
certain  defects  of  the  eye  which  are  quite  common. 
The  principles  involved  in  the  construction  of  the  nor- 
mal eye  may  be  still  further  enforced  and  illustrated  by 
an  explanation  of  these  defects.  Let  it  be  observed, 
however,  that  these  defects  must  not  be  regarded  as  the 
result  of  imperfect  work  on  the  part  of  Nature,  but 
rather  as  the  effects  of  misuse  of  the  eye,  accumulated 
by  inheritance  for  many  generations.  They  do  not 
occur  in  animals,  nor  in  the  same  degree  in  savage 
races ;  and  most  of  them  are  also  very  rare  in  persons 
living  for  many  generations  in  the  country. 

The  most  important  of  these  defects  are  myopy  and 
presbyopy. 

Myopy,  Brachymetropy,  or  Near  -  Sightedness.— The 
normal  or  emmetropic  eye  adjusts  itself  perfectly  for 
all  distances,  from  about  "five  inches  to  infinity.  It 


DEFECTS   OF   THE  EYE   AS  AN  INSTRUMENT.  47 


makes  a  perfect  image  of  objects  at  all  these  distances. 
This  is  called  its  range  of  distinct  vision.  It  has  but  one 
limit,  viz.,  the  nearer  limit  of  five  inches.  ^Kow  in  the 
passive  state  of  the  eye,  as  for  instance  in^gakii^oh^^ •;„. 
vacancy,  or  when  the  eye  is  taken  out  of  the  socket  as 
a  dead  instrument,  it  is  prearranged  for  perfect  image 
of  objects  at  an  infinite  distance.  Its  focus  of  parallel 
rays  in  a  passive  state  is  on  the  retina.  For  all  nearer 
objects,  a  voluntary  effort  is  necessary  to  throw  the 
image  on  the  retina,  which  effort  is  greater  as  the 
object  is  nearer,  until  it  is  limited  at  the  distance  of 
about  five  inches.  The  normal  eye,  therefore,  is  like 
a  camera,  which,  when  pushed  up  as  much  as  possible, 
is  arranged  for  making  a  perfect  image  of  sun,  or  moon, 
or  a  distant  landscape,  but  can  by  drawing  the  tube  be 
adjusted  to  shorter  and  shorter  distances  up  to  five 
inches,  but  not  nearer. 

The  myopic  eye,  on  the  other  hand,  is  not  pre- 
arranged for  perfect  image  of  distant  objects.  Its  focus 
for  distant  objects  (focus  of  parallel  rays)  is  not  on  the 
retina,  but  in  front  of  it.  The  refractive  power  of  the 
lenses  in  their  passive  state  is  too  great,  or  else  the  re- 
ceiving screen  (retina)  may  be  regarded  as  too  far  back 
from  the  lens,  viz.,  at  S"  S",  Fig.  7,  page  27.  The  rays 
have  already  reached  focus,  crossed,  and  again  spread 
out  before  they  reach  the  retina.  An  object  must  be 
brought  much  nearer  before  its  perfect  image  will  be 
thrown  on  the  retina.  Within  this  farther  limit  of 
perfect  image,  however,  it  has  its  own  range  of  adjust- 
ment, like  the  normal  eye.  The  range  of  the  normal 
eye  is  from  infinite  distance  to  five  inches.  In  the 
myopic  eye  the  range  may  be  from  a  yard  to  four 
inches,  or  from  a  foot  to  three  inches,  or  from  six  inches 
to  two  inches,  or  even  from  three  inches  to  one  inch, 
8 


48  MONOCULAR  VISION. 

according  to  the  degree  of  myopy.  The  amount  of 
ocular  adjustment  or  change  in  the  lens  to  effect  these 
ranges  is  as  great  as  for  the  normal  range  from  infinite 
distance  to  five  inches,  but  the  latter  is  a  far  more  use- 
ful range.  The  myopic  eye,  therefore,  is  like  a  camera 
which  was  never  intended  to  be  used  for  taking  distant 
objects,  which,  therefore,  when  shortened  to  the  greatest 
degree,  is  still  too  long  in  the  chamber  for  distant  ob- 
jects, but  is  adapted  only  for  near  objects  within  a  cer- 
tain limited  range. 

It  is  evident,  then,  that,  the  defect  of  the  myopic 
eye  being  too  great  refractive  power  of ^  the  lens  in  a 
passive  state,  this  defect  may  be  remedied  by  the  use  of 
concave  glasses,  with  concavity  just  sufficient  to  correct 
the  excess  of  refractive  power,  and  therefore  to  throw 
the  image  of  distant  objects  back  to  the  retinal  screen 
in  the  passive  state  of  the  eye.  The  eye  then  adjusts 
itself  to  all  nearer  distances,  and  becomes  in  all  respects 
a  normal  eye.  From  the  nature  of  the  defect  (structural 
defect),  it  is  evident  that  the  glasses  must  be  worn  habit- 
ually. 

Presbyopy,  or  Old-Sightedness. — This  defect  is  often 
called  long-sightedness,  or  far-sightedness ;  but  this  is 
a  misnomer,  based  on  a  misconception  of  its  true  na- 
ture. It  is  obviously  impossible  to  have  an  eye  more 
long-sighted  than  the  normal  eye,  for  this  defines  with 
perfect  distinctness  the  most  distant  objects,  such  as 
the  moon  or  the  sun  when  the  dazzling  effect  is  pre- 
vented by  smoked  glass.  It  is  usually  regarded  as  a 
defect  the  reverse  of  near-sightedness.  As  near-sighted- 
ness is  the  result  of  too  great  refractive  power  in  a  pas- 
sive condition,  so  this  is  supposed  to  be  a  too  small  refrac- 
tive power  in  the  same  condition.  As  the  myopic  eye 
throws  the  focus  of  parallel  rays  in  front  of  the  retina, 


DEFECTS  OF  THE  EYE  AS  AN  INSTRUMENT.     49 

so  it  is  supposed  the  presbyopic  eye  throws  the  focus  of 
parallel  rays  behind  the  retina,  because  the  retina  is  too 
near  the  lens,  at  AS"  /Sv/,  Fig.  7,  page  27.  It  is  further 
supposed  that  the  change  which  takes  place  with  age  is 
a  flattening,  and  therefore  a  loss  of  refractive  power,  of 
the  lenses  of  the  eye.  It  is  constantly  asserted,  there- 
fore, that  the  myopic  eye  may  be  expected  to  become 
normal  with  age. 

Now  this  view  of  the  nature  of  presbyopy  is  wholly 
wrong.  The  presbyopic  eye  sees  distant  objects  per- 
fectly well,  and  precisely  like  the  normal  eye.  Its  pas- 
sive structure  is  therefore  unaltered.  It  makes  a  perfect 
image  of  distant  objects  on  the  retina,  like  the  normal 
eye.  Its  focus  of  parallel  rays  is  on  the  retina,  not  be- 
hind it.  It  is  therefore  normal  in  its  passive  state,  or 
in  its  structure.  The  defect,  therefore,  consists  not  in 
a  change  of  the  structure  which  originally  adapted  it 
to  the  imaging  of  distant  objects,  but  in  the  loss  of 
power  to  adjust  for  near  objects.  And  this  loss  of 
adjusting  power  is,  again,  probably  the  result  of  loss  of 
the  elasticity  of  the  crystalline  lens.  In  the  normal 
young  eye,  when  the  ciliary  muscle  pulls  forward  the 
lens  curtain,  and  thus  relaxes  its  tension,  the  lens  by  its 
elasticity  swells  and  thickens,  and  becomes  more  refrac- 
tive. In  the  presbyopic  eye,  the  ciliary  muscle  pulls, 
and  the  curtain  or  capsule  relaxes  its  tension,  in  vain ; 
the  lens,  for  want  of  elasticity,  does  not  swell  out. 
Therefore  the  remedy  for  presbyopy  is  the  use  of  con- 
vex glasses,  not  habitually,  not  in  looking  at  distant 
objects,  but  only  in  looking  at  or  imaging  near  objects. 
The  putting  on  of  convex  glasses  does  not  make  the 
presbyopic  eye  normal,  as  the  use  of  concave  glasses 
makes  the  myopic  eye  ;  therefore  they  can  not  be  worn 
habitually.  In  looking  at  near  objects,  it  uses  glasses ; 


50  MONOCULAR  VISION. 

in  looking  at  distant  objects,  the  glasses  are  removed. 
Myopy  is  a  structural  defect ;  presbyopy  is  a  functional 
defect.  One  is  a  defect  of  prearrangement  of  the  instru- 
ment ;  the  other  is  a  loss  of  power  to  adjust  the  instru- 
ment. To  compare  with  the  camera  again  :  the  presby- 
opic  eye  is  like  a  camera  which  was  originally  arranged 
for  distant  objects,  and  by  drawing  the  tube  could  be 
adjusted  for  near  objects  also,  but,  through  age  and 
misuse  and  rust,  the  draw-tube  has  become  so  stiff  that 
the  apparatus  for  adjustment  no  longer  works.  It  still 
operates  well  for  distant  objects,  but  can  not  be  adjusted 
for  nearer  objects.  If  we  desire  to  image  a  near  object 
in  such  a  camera,  obviously  we  must  supplement  its 
lens  with  another  convex  lens. 

From  what  has  been  said  it  is  evident  that  the 
myopic  eye  does  not  improve  with  age,  and  finally 
become  normal,  as  many  suppose.  Myopic  persons 
continue  to  wear  glasses  of  the  same  curvature  until 
sixty  or  seventy  years  of  age.  I  have  never  known  a 
myopic  person  who  discontinued  the  use  of  glasses  as 
he  grew  older.  The  same  change,  however,  takes  place 
in  the  myopic  as  in  the  normal  eye,  i.  e.,  the  loss  of  ad- 
justment. In  all  young  eyes  there  is  a  range  of  adjust- 
ment between  a  nearer  and  a  farther  limit ;  in  the  nor- 
mal eye  it  is  between  five  inches,  near  limit,  and  infinite 
distance,  the  farther  limit  (if  limit  it  can  be  called) ;  in 
the  myopic  eye  the  nearer  limit  may  be  two  inches,  the 
farther  limit  four  inches,  or  it  may  be  between  three 
and  six  inches,  or  four  inches  and  one  foot,  according 
to  the  degree  of  myopy.  Now,  with  advancing  age, 
the  nearer  limit,  i.  e.,  the  limit  of  adjustment,  recedes. 
In  the  normal  eye  it  is  first  eight  inches,  then  one  foot, 
then  three  feet,  etc.,  until,  when  adjustment  is  entirely 
^artner  limit  and  there  is  but  one 


DEFECTS  OF  THE  EYE  AS  AN  INSTRUMENT.  51 

distance  of  distinct  vision ;  but  the  farther  limit,  i.  e., 
structural  limit,  does  not  change.  So  also  in  the  my- 
opic eye,  with  advancing  age,  the  nearer  limit  or  limit 
of  adjustment  recedes,*  but  not  the  farther  limit  or 
structural  limit.  This  remains  the  same.  But,  as  this 
was  always  too  near  for  useful  vision,  glasses  must  still 
be  worn.  Thus  it  is  evident  that  myopy  and  presbyopy 
may  exist  in  the  same  individual. 

In  extreme  old  age,  when  the  tissues  begin  to  break 
down,  it  is  probable  that  some  flattening  of  the  eye 
may  take  place.  To  such  persons  it  would  be  necessary 
to  wear  convex  glasses,  even  for  distant  objects.  But 
this  is  not  ordinary  presbyopy.  In  fact,  it  is  probable 
that  most  of  such  cases  belong  to  the  next  category. 

Hypermetropy. — We  have  dwelt  on  the  two  most 
common  defects  of  the  eye,  but  there  are  others  less 
common,  which  must  be  briefly  characterized.  Hyper- 
metropy is  the  true  opposite  of  myopy.  Like  the  latter, 
it  is  a  structural  defect,  but  in  the  opposite  direction. 
In  this  case  the  lens  is  not  sufficiently  refractive  for 
the  length  of  the  chamber,  or  the  receiving  screen  is  too 
near  (at  $'  /#',  Fig.  7)  for  the  refractive  power  of  the 
lens.  Therefore  the  focus  of  parallel  rays  is  behind 
the  retina  in  a  passive  state  of  the  eye.  The  hyper- 
metropic  eye  when  young  usually  sees  well  at  a  distance, 
but  not  near  at  hand,  and  therefore  it  is  apt  to  be  con- 
founded with  presbyopy.  The  reason  is,  that  a  slight 
adjustment  adapts  the  eye  for  perfect  retinal  image  of 
distant  objects ;  but  the  near  limit  of  its  range  of  ad- 
justment is  much  farther  off  than  in  the  normal. 
When,  however,  the  hypermetropic  eye  loses  its  power 
of  adjustment  with  age,  then  even  distant  objects  can 
not  be  seen  distinctly.  Such  persons,  therefore,  while 
young,  should  habitually  wear  slightly  convex  glasses, 


52  MONOCULAR  VISION. 

which  mate  their  eyes  normal.  When  they  grow  old, 
they  are  compelled  to  have  two  pairs  of  glasses,  one  for 
distant  objects  and  one  for  near  objects  ;  one  for  walk- 
ing and  one  for  reading.  The  liypermetropic  eye  may 
be  compared  to  a  camera  which,  when  entirely  pushed 
up,  is  too  short  for  the  imaging  of  any  objects  what- 
ever. 33y  drawing,  it  may  be  adjusted  for  distant  ob- 
jects, but  not  for  near  objects. 

Astigmatism. — The  form  of  a  perfect  eye  is  that  of 
a  spheroid  of  revolution  about  the  optic  axis.  Its  re- 
fraction in  a  horizontal  and  a  vertical  plane  will  be 
equal.  This  is  necessary  to  bring  all  rays  to  a  perfect 
point  at  the  same  distance.  But  eyes  are  found  in  which 
the  horizontal  curvature  of  the  cornea  or  of  the  crys- 
talline, or  both,  is  different  from  the  vertical  curvature. 
Such  eyes  are  said  to  be  astigmatic,  because  the  rays 
from  any  radiant  are  brought  to  a  focal  line,  instead  of 
a  focal  point.  A  very  slight  degree  of  astigmatism  is 
not  uncommon,  and  often  exists  unknown  to  the  patient. 


CHAPTER  IV. 

EXPLANATION  OF  PHENOMENA  OF  MONOCULAR  VISION. 
SECTION  I.— STRUCTURE   OF  THE  RETINA. 

WE  have  thus  far  treated  of  the  eve,  and  compared 
it  with  the  camera,  purely  as  an  optical  instrument,  con- 
trived to  form  an  image  upon  a  receiving  screen  suit- 
ably placed.  We  have  also  treated  of  the  defects  of 
the  eye,  as  much  as  possible,  from  the  same  physical 
point  of  view  as  defects  of  an  instrument.  But  in  both 
the  camera  and  the  eye  the  image  is  only  a  means  to 
accomplish  a  higher  purpose,  viz.,  to  make  a  photo- 
graphic picture  in  the  one  case  and  to  accomplish  vision 
in  the  other.  We  have  thus  far  spoken  as  much  as 
possible  only  of  an  insensitive  screen,  the  ground-glass 
plate  in  the  one  case  and  the  dead  retina  in  the  other. 
But  in  both,  when  accomplishing  their  real  work,  we 
have  a  sensitive  screen,  in  which  wronderful  changes 
take  place,  viz.,  the  iodized  plate  in  the  one  and  the 
living  retina  in  the  other.  In  order  to  understand  the 
real  function  of  the  eye  in  the  living  animal,  it  is  neces- 
sary that  we  study  the  structure  and  functions  of  the 
retina. 

Structure  of  the  Retina. — The  retina,  as  already 
stated,  page  22,  is  a  thin  membranous  expansion  of  the 


54: 


MONOCULAR  VISION. 


optic  nerve.  These  nerves,  arising  from  the  optic  lobes 
of  the  midbrain,  appear  first  beneath  the  base  of  the 
brain  as  the  optic  roots,  r  r' ,  Fig.  20,  converge,  unite, 
and  partially  cross  their  fibers  at  the  optic  chiasm,  ch  / 
then,  again  diverging,  enter  the  conical  eye-sockets  a 
little  to  the  interior  of  the  point ;  then  pass  through  the 
midst  of  the  fatty  cushion  behind  the  eye,  surrounded 

FIG.  20. 


A  VIEW  OF  THE  Two  EYES,  WITH  OPTIO  NERVES.— ch,  optic  chiasm ;  r  r',  nerve- 
roots  ;  n  and  »',  right  and  left  optic  nerves.    (After  Helmholtz.) 

by  the  diverging  recti  muscles,  and  finally  penetrate 
the  sclerotic  at  a  point  about  one  eighth  of  an  inch  to 
the  inside  of  the  axes ;  then  spread  out  all  over  the 
interior  of  the  ball  as  an  innermost  coat,  immediately 
in  contact  with  the  vitreous  humor,  and  extend  as  far 
forward  as  the  ciliary  processes,  or  nearly  to  the  iris. 
The  wide  extent  of  this  expansion  and  its  hollow  con- 


STRUCTURE   OF  THE  RETINA. 


55 


cave  form  are  necessary  to  give  wideness  to  the  field  of 
view.  By  this  means  rays  from  objects,  not  only  in 
front  but  far  to  the  right  and  left,  above  and  below, 
fall  upon  and  impress  the  retina. 

The  thickness  of  this  nervous  expansion  is  about 
one  hundredth  of  an  inch,  or  about  the  thickness  of 
thin  cardboard,  at  the  bottom  or  thickest  part,  but  thins 
to  one  half  that  amount  on  the  anterior  margins ;  yet, 
under  the  microscope,  a  section  through  the  thickness 
shows  that  it  is  very  complex  in  its  structure,  being 
composed  of  several  very  distinct  layers.  We  may  first 
represent  it  on  a  smaller  scale  as  composed  of  three 
principal  layers  :  First,  the  innermost  layer,  /*,  Fig.  21, 

FIG.  21. 


GENERALIZED  SECTION  OF  RETINA,  ETC.—  0,  optic  nerve;  S,  sclerotic;  ch,  choroid;  X, 
retina;  ft,  bacillary  layer;  g,  granular  and  cellular  layer;  /,  fibrous  layer;  V,  vitre- 
ous humor ;  c,  central  spot. 

in  contact  with  the  vitreous  humor,  F,  is  composed 
wholly  of  fine  interlaced  fibers  of  the  optic  nerve.  This 
nerve,  0,  is  seen  to  pierce  the  sclerotic  and  the  other 
layers  of  the  retina,  and  then  to  spread  out  as  an  inner- 
most layer.  Second,  outermost  of  all,  and  therefore  in 
contact  with  the  choroid,  cA,  is  a  remarkable  layer,  com- 
posed of  cylindrical  rods,  like  pencils  set  on  end.  This 
is  called  the  bacillary  layer  (bacillum,  a  small  rod),  or 


56 


MONOCULAR  VISION. 


layer  of  rods,  b.  Third,  between  these  is  found  a  layer 
composed  of  granules  and  nucleated  cells,  g.  This  may 
be  called  for  the  present  the  granular  and  nuclear  layer. 


FIG.  22. 


ENLARGED  SECTION  OF  KETINA  (after  Schultze).— A,  general  view ;  .5,  nervous  ele- 
ments ;  a,  bacillary  layer ;  c,  external  nuclear  layer ;  d,  external  granular  layer ;  e, 
internal  nuclear  layer;  /,  internal  granular  layer;  0,  ganglionic  layer;  h,  fibrous 
layer,  consisting  of  fibers  of  optic  nerve. 


STRUCTURE   OF  THE  RETINA.  57 

Further,  it  will  be  seen  that  these  layers  exist,  all 
three,  in  every  part  of  the  retina  except  two  spots. 
These  are  the  spots  where  the  optic  nerve,  0,  enters, 
and  the  central  spot,  <?,  which  is  in  the  axis  of  the  eye. 
Where  the  optic  nerve  enters,  of  course,  no  other  layer 
can  exist  except  the  fibrous  layer.  In  the  central  spot 
the  fibrous  layer  is  wholly  wanting,  and  the  granular 
and  nuclear  layer  is  almost  wanting,  so  that  the  retina 
is  here  almost  reduced  to  the  bacillary  layer.  For  this 
reason  this  spot  forms  a  depression  in  the  retina. 

But  the  extreme  importance  of  the  retina  requires 
that  these  layers  be  examined  more  closely.  For  this 
a  much  greater  enlargement  is  necessary.  Fig.  22  rep- 
resents such  enlargement.  The  fibrous  layer,  A,  requires 
no  further  description ;  but  the  granular  and  nuclear 
layer  is  seen  to  be  composed  of  two  distinct  layers  of 
small  granules,  d  and  f,  and  two  layers  of  large  nucle- 
ated cells,  c  and  <?,  and  a  layer  of  very  large  nucleolated 
cells,  g,  from  which  go  out  branching  fibers.  These  are 
multipolar  cells,  or  ganglia.  It  is  further  seen  that  the 
bacillary  layer  is  composed  of  two  kinds  of  elements, 
viz.,  slender  cylindrical  rods  and  larger  cone-like  bodies. 
These  are  called  rods  and  cones.  It  is  seen,  still  further, 
that  all  these  different  elements  of  the  retina  are  in  con- 
tinuous connection  with  each  other,  and  with  the  fibers 
of  the  optic  nerve. 

The  bacillary  layer  is  of  the  extremest  interest.  It 
consists  mostly  of  rods,  but  among  these  are  distributed 
the  larger  cones,  as  in  Fig.  23,  A.  As  we  approach 
the  central  spot  the  cones  become  more  numerous,  as 
seen  in  B.  In  the  depression  of  the  central  spot  (fovea 
centralis)  we  find  only  cones,  and  these  are  of  much 
smaller  size  than  those  in  other  parts  of  the  retina,  as 
seen  in  C.  The  rods  are  about  ^-J-^  inch  in  length  and 


58  MONOCULAR  VISION. 


inch  in  diameter.  The  cones  are  shorter  and 
about  three  times  thicker  than  the  rods,  except  in  the 
central  depression,  where  they  are  nearly  as  small  as  the 
rods,  being  there  only  TTrfoir  inc^  ^n  diameter.  In  this 
spot,  therefore,  there  are  probably  no  less  than  one  mil- 
lion cones  in  a  square  Y1^  inch. 


FIG.  23. 


BACILLART  LAYER,  VIEWED  FROM  THE  OUTSIDE  SURFACE.— A,  appearance  of  usual 
surface ;  E,  appearance  of  surface  of  the  raised  margin  of  yellow  spot ;  C,  surface  of 
central  spot. 

Distinctive  Functions  of  the  Layers. — As  the  distinc- 
tive functions  of  the  several  sub-layers  of  the  middle 
layer  (granular  and  nuclear)  are  unknown,  we  will  treat 
of  only  the  three  layers — inner,  middle,  and  outer.  The 
outer  layer  of  rods  and  cones  (bacillary)  is  undoubtedly 
the  true  receptive  layer,  which  corresponds  to  the  iodized 
film  of  the  sensitized  plate  of  the  camera.  These  rods 
and  cones  receive  and  respond  to  the  vibrations  of  light ; 
they  co-vibrate  with  the  undulations  of  the  ether. 
The  inner  or  fibrous  layer  conducts  the  received  im- 
pression to  the  optic  nerve ;  for  each  rod  and  cone  is 
connected  by  a  slender  thread,  continuous  with  nucle- 
ated cells  of  the  granular  layer  and  a  fiber  of  the  fibrous 
layer.  The  fibrous  layer  may,  in  fact,  be  regarded  as  a 
layer  of  conducting  threads  coming  from  the  rods  and 
cones,  which  threads  are  then  gathered  into  a  cord  or 
cable,  the  optic  nerve,  which  in  its  turn  finally  conducts 
the  impression  to  the  brain.  The  function  of  the  mid- 
dle layer  is  more  obscure ;  but  nucleated  nerve-cells, 
and  especially  multipolar  cells,  are  always  generators  or 


STRUCTURE   OF  THE   RETINA.  59 

originators  of  nerve-force.  They  evidently  have  an 
important  function.  They  probably  act  as  little  nerve- 
centers  ;  and  many  unconscious,  involuntary,  or  reflex 
acts  of  vision  are  probably  performed  by  their  means, 
without  referring  the  sensation  to  the  brain. 

The  manner  in  which  the  whole  apparatus  operates 
is  briefly  as  follows  :  The  light  penetrates  through  the 
retina  until  it  reaches  the  outer  layer  of  rods  and  cones. 
These  are  specially  organized  to  respond  to  or  co-vibrate 
with  the  undulations  of  light.  These  vibrations  are 
carried  through  the  connecting  threads  to  the  fibrous 
layer,  then  through  the  fibers  of  this  layer  to  the  optic 
nerve,  then  along  the  fibers  of  the  optic  nerve  to  the 
gray  matter  of  the  brain,  where  they  finally  determine 
changes  which  emerge  into  consciousness  as  the  sensa- 
tion of  light. 

That  we  have  correctly  interpreted  the  function  of 
the  layer  of  rods  and  cones  is  rendered  probable  not 
only  by  its  very  remarkable  and  complex  structure, 
adapting  it  to  responsive  vibrations,  but  also  by  the 
peculiar  properties  of  two  spots  on  the  retina  on  which 
all  the  layers  do  not  co-exist.  Just  where  the  optic 
nerve  enters,  as  shown  in  Fig.  21,  page  55,  the  bacillary 
layer  is  necessarily  wanting,  and  it  is  the  only  spot  in 
which  this  is  the  case.  Now,  Ms  spot  is  blind  (see  page 
78).  Again,  just  in  the  axis  of  the  globe,  or  what 
might  be  called  the  south  pole  of  the  eye,  is  the  central 
spot  or  central  pit.  In  this  spot  is  wanting  the  fibrous 
]ayer  and  the  whole  of  the  middle  layer,  except  the 
multipolar  cells.  The  bacillary  layer  is  here,  therefore, 
directly  exposed  to  the  action  of  light.  Now,  this  is 
the  most  sensitive  spot  of  the  retina. 

Perception  of  Color.— Color,  like  musical  pitch,  con- 
sists of  an  infinite  number  of  kinds  and  shades;  but 


60  MONOCULAR  VISION. 

these  may  be  reduced  to  a  few  primary  kinds,  by  the 
mixture  of  which  the  intermediate  shades  may  be  sup- 
posed to  be  made.  Newton  made  seven  primary  colors 
in  the  solar  spectrum;  but  though  these,  and  indeed 
many  more,  may  be  considered  distinct  from  the  physi- 
cal point  of  view,  since  they  are  the  result  of  different 
rates  of  ethereal  vibration,  yet  they  can  not  be  all  con- 
sidered as  primarily  distinct  sensations.  Brewster  re- 
duced all  color-sensations  to  three  primary,  viz.,  red, 
yellow,  and  blue.  Young  made  them  red,  green,  and 
violet.  This  latter  view  is  adopted  by  Helmholtz  and 
most  modern  writers. 

Recently,  however,  Hering  *  has  reinvestigated  the 
whole  subject  with  great  acuteness,  from  the  purely  phys- 
iological instead  of  physical  point  of  view,  and  arrives 
at  different  results.  Hering  includes  white  and  Hack 
among  his  primary  color-sensations,  making  six  in  all. 
But,  leaving  out  these  as  belonging  rather  to  the  cate- 
gory of  shades  or  nuances,  according  to  Hering  there 
are  four  and  only  four  primary  color-sensations  essen- 
tially distinct  from  each  other,  viz.,  red,  yellow,  green, 
and  blue.  Aside  from  all  physical  considerations,  un- 
doubtedly this  is  true.  These  four  colors  are  essen- 
tially distinct  and  irresolvable  into  any  mixture  of  oth- 
ers. Again,  according  to  Hering,  these  four  are  re- 
ducible to  two  complementary  pairs,  viz.,  red  and  green 
on  the  one  hand,  and  yellow  and  blue  on  the  other. 
This  is  also  undoubtedly  true.  Finally,  according  to 
Hering,  complementary  colors  are  the  result  of  opposite 
affections  of  the  retina,  so  that  there  are  only  two  essen- 
tially distinct  color-affections  of  the  retina,  which,  with 
their  opposites,  produce  the  two  pairs  of  complementary 
colors  :  the  one  with  its  opposite  produces  red  and  green ; 

*  Ilcring,  "  Zur  Lchrc  von  Licht-Sinnc,"  Wien,  1878. 


STRUCTURE   OF   THE   RETINA.  61 

the  other  with  its  opposite,  yellow  and  blue.  This, 
though  more  doubtful,  seems  a  probable  cause  of  com- 
plementariness. 

Theory  of  Color-Perception. — Color-perception  is  un- 
doubtedly a  simple  perception,  and  irresolvable  into 
any  other.  It  must,  therefore,  have  its  basis  in  retinal 
structure.  Since  light  is  perceived  by  co-vibration  of 
retinal  elements,  and  since  the  different  colors  have 
different  rates  of  vibration,  there  must  be  a  correspond- 
ing structure  of  the  retinal  elements,  by  means  of  which 
they  co-vibrate  with  each  of  these  colors.  In  the  ear 
different  rates  of  aerial  vibration  (musical  pitch)  are  per- 
ceived by  means  of  rods  of  different  lengths  (rods  of 
Corti),  which  co-vibrate,  each  wTith  its  own  pitch.  It 
seems  probable,  therefore,  that  different  rods  or  cones  co- 
vibrate  with  different  rates  of  ethereal  undulations,  i.  e., 
with  different  colors.  This  is  the  commonly  received 
view,  brought  forward  first  by  Young.  It  is  supposed 
that  there  are  three  kinds  of  rods  or  cones,  which  sever- 
ally co-vibrate  with  the  three  primary  colors  of  Young. 
One  kind  responds  to  the  slower  vibrations  of  red,  anoth- 
er kind  to  those  of  green,  and  still  another  to  the  more 
rapid  vibrations  of  violet.  "When  two  kinds  vibrate, 
intermediate  colors  are  perceived.  When  all  vibrate 
together,  then  white  light  is  perceived.  Or,  to  express 
it  differently,  intermediate  colors  produce  vibration  of 
two  kinds,  white  light  of  all  kinds,  of  rods.  Or,  if  we 
adopt  the  theory  of  Hering  in  regard  to  the  primary 
colors,  one  kind  of  rod  or  cone  responds  to  red  and 
green,  another  kind  to  yellow  and  blue. 

Yery  recently  Stanly  Hall  has  proposed  a  theory 
which  seems  even  more  probable.*  He  believes  that 
color  is  perceived  by  the  cones  alone ;  further,  that 

*  "American  Academy  of  Science  and  Art,"  vol.  xiii,  p.  402  (1878). 


62  MONOCULAR  VISION. 

different  parts  of  the  same  cone  vibrate  with  different 
degrees  of  rapidity,  and  therefore  respond  to  different 
colors,  and  that  the  conical  form  is  adapted  for  this 
purpose.  In  order  to  gain  clearer  conception,  we  may 
imagine  each  cone  to  be  made  up  of  a  number  of  but- 
tons of  graduated  sizes  joined  together.  These  buttons, 
on  account  of  their  different  sizes,  would  vibrate  with 
different  degrees  of  rapidity,  and  therefore  co-vibrate 
with  different  colors.  White  light,  he  supposes,  vibrates 
the  whole  series ;  red  light,  the  thicker,  and  violet,  the 
thinner,  portion  of  the  series ;  or,  taking  Bering's  view 
of  the  primary  colors,  we  may  imagine  that  red  and 
green  rays  affect  one  portion,  and  yellow  and  blue  rays 
another  portion,  of  the  same  cone. 

The  subject  of  the  mechanism  of  color  perception, 
however,  is  yet  in  the  region  of  speculation,  though 
probably  of  profitable  speculation.  To  pursue  it  any 
further  would  be  unsuited  to  the  character  of  this  trea- 
tise. 

Daltonism,  or  Color-Blindness.— Many  persons  lack  a 
nice  discrimination  of  shades  of  color.  Such  persons 
see  colors  perfectly  well,  but,  from  want  of  attention  or 
culture,  have  not  learned  to  nicely  discriminate  and 
name  them.  This  must  not  be  confounded  with  color- 
blindness. The  color-blind  do  not  see  some  colors  as 
colors  at  all.  The  defect  is  not  one  of  culture,  but  of 
sensation.  We  can  best  explain  it  by  comparing  the 
eye  and  ear. 

The  limits  of  the  perception  of  sound- vibrations  are 
very  wide,  viz.,  more  than  eleven  octaves.  The  limits 
of  perception  of  light-vibrations  are  far  more  restricted, 
viz.,  only  a  little  more  than  one  octave.  Now  in  many 
ears  the  extreme  limits  are  not  perceived  ;  but  this  is  not 
considered  a  defect,  because  there  is  no  special  use  for 


STRUCTURE  OF  THE   RETINA.  63 

the  extremes!  range.  So  in  the  eye.  Even  the  narrow 
limits  of  .the  normal  eye  are  sometimes  not  reached  ;  but 
in  this  case  the  usefulness  of  the  whole  range  makes  it 
a  serious  defect.  This  is  color-blindness.  In  the  ear 
the  vibrations  most  commonly  unperceived  are  at  the 
upper  end  of  the  scale.  In  the  eye  it  is  usually  the 
lower  end  of  the  scale  which  is  defective,  viz.,  red,  or 
red  and  green.  The  color-blind  see  yellow  and  blue, 
but  not  red  and  green. 

This  defect  was  first  brought  to  scientific  notice  by 
the  celebrated  chemist  Dalton,  and  after  him  has  often 
been  called  Daltonism.  The  peculiarities  of  Dalton's 
vision  were  carefully  investigated  by  Sir  John  Herschel, 
and  the  first  scientific  explanation  was  given  by  him. 
Adopting  the  view  of  Young  of  three  primary  colors, 
Herschel  regarded  normal  vision  as  trichromic,  but  the 
vision  of  Dalton  as  dichromic,  the  red  being  wanting. 
This  view  certainly  explained  the  most  striking  phe- 
nomena of  color-blindness,  but  it  does  not  explain  the 
fact  that  green  is  wanting  as  well  as  red.  As  shown  by 
Pole  *  (who  is  himself  color-blind),  the  phenomena  are 
far  more  perfectly  explained  on  Hering's  view  of  the 
primary  colors ;  and  conversely,  the  phenomena  of  color- 
blindness are  a  powerful  argument  in  favor  of  Hering's 
view.  Of  the  two  pairs  of  complementary  colors  of 
Hering,  one  pair,  viz.,  the  red-green,  is  wanting  in  the 
color-blind,  while  the  other  pair,  yellow-blue,  is  perceived 
as  in  normal  vision.  The  colors  and  shades,  therefore, 
which  are  perceived  by  the  color-blind  are :  1,  black  and 
white,  and  all  intermediate  shades  of  gray  ;  2,  yellow  in 
all  its  shades  ;  and,  3,  blue  in  all  its  shades.  A  pure  red 
seems  to  them  a  dark  gray  ;  but  if  mixed  with  yellow,  as 

*  "Nature,"  20,  pp.  477,  611,  637  (1879);  "Contemporary  Review," 
May,  1880. 


64  MONOCULAR  VISION. 

are  most  reds,  it  appears  yellow  mixed  with  gray,  or  a 
kind  of  brown •  or  if  mixed  with  blue  (purple),  it  ap- 
pears as  blue  mixed  with  gray,  or  slate-Hue.  A  pure 
green  appears  simple  gray  •  a  yellow-green,  yellow  mixed 
with  gray — i.  e.,  brown  /  and  a  blue  green,  slate-Hue. 

The  cause  of  this  defect  of  vision  is,  of  course,  a 
defect  of  retinal  structure.  If  we  admit  that  the  rods 
and  cones  are  the  responsive  elements,  and  that  differ- 
ent kinds  of  rods  or  cones  respond  to  different  primary 
colors,  then  in  the  retina  of  the  color-blind  the  rods  or 
cones  responding  to  red  and  green  are  wanting ;  or, 
by  Hall's  theory,  the  cones  are  so  shaped  that  they  re- 
spond to  only  one  complementary  pair,  viz.,  to  yellow 
and  blue. 


SECTION  II.— FUNCTION  OF  THE  RETINA,  AND  EXPLANATION 
OF  THE  PHENOMENA  OF  MONOCULAR  VISION. 

There  is  ^  certain  peculiarity  in  the  general  func- 
tion of  the  retina,  optic  nerve,  and  associated  brain 
apparatus,  which  must  now  be  explained  and  clearly 
apprehended,  in  order  to  understand  the  phenomena 
of  vision. 

Law  of  Outward  Projection  of  Retinal  Impressions.— 
An  image  is  formed  on  the  retinal  screen.  We  have 
seen  that  the  whole  object  of  the  complex  arrangement 
of  lenses  placed  in  front  of  the  retina  is  the  formation 
of  images.  But  we  do  not  see  the  retinal  images.  We 
do  not  see  anything  in  the  eye^  but  something  outside 
in  space.  It  would  seem,  then,  that  the  retinal  image 
impresses  the  retina  in  a  definite  way ;  this  impression 
is  then  conveyed  by  the  optic  nerve  to  the  brain,  and 
determines  changes  there,  definite  in  proportion  to  the 


FUNCTION   OF  THE  RETINA.  65 

distinctness  of  the  retinal  image ;  and  then  the  brain 
or  the  mind  refers  or  projects  this  impression  outward 
into  space  as  an  external  image,  the  sign  and  facsimile 
of  an  object  which  produces  it.  We  shall  see  hereafter 
how  important  it  is  that  we  regard  what  we  see  as  ex- 
ternal images,  the  signs  of  objects  which  produce  them, 
and  these  external  images  themselves  as  projections 
outward  of  retinal  images. 

This  law  of  outward  projection  is  so  important  that 
we  will  stop  a  moment  to  show  that  it  is  not  a  new  law 
specially  made  for  the  sense  of  sight,  but  only  a  modi- 
fication of  a  general  law  of  sensation.  After  doing  so, 
we  will  proceed  to  illustrate  by  many  phenomena,  so  as 
to  fix  it  well  in  the  mind. 

Comparison  with  Other  Senses. — The  general  law  of 
sensation  is,  that  irritation  or  stimulation  in  any  portion 
of  the  course  of  a  sensory  fiber  is  referred  to  its  periph- 
eral extremity.  Thus,  if  the  sciatic  nerve  bo  laid  bare 
in  the  upper  thigh,  and  then  pinched,  the  pain  is  felt, 
not  at  the  part  injured,  but  at  the  termination  of  the 
nerve  in  the  feet  and  toes.  If  the  ulnar  nerve  be 
pinched  in  the  hollow  on  the  inner  side  of  the  point 
of  the  elbow,  pain  is  felt  in  the  little  and  ring  fingers, 
where  this  nerve  is  distributed.  In  amputated  legs, 
as  is  well  known,  the  sense  of  the  presence  of  a  foot 
remains,  and  often  severe  neuralgic  pains  are  felt  in  the 
feet  and  toes.  The  pain,  which  in  this  case  is  caused 
by  a  diseased  condition  of  the  nerves  at  the  point  of 
amputation,  is  referred  to  the  place  where  the  diseased 
fibers  were  originally  distributed.  In  nerves  of  com- 
mon sensation,  therefore,  injury  or  disease,  or  stimu- 
lation of  any  kind  in  any  part,  is  referred  to  the 
peripheral  extremity  of  the  nerve-fibers.  Now  the 
peculiarity  of  the  optic  nerve  is,  that  it  refers  impres- 


66  MONOCULAR  VISION. 

sions  not  to  its  peripheral  extremity  only,  but  beyond 
into  spate. 

But  when  we  find  great  differences  in  the  functions 
of  tissues,  such  as  occur  in  this  case,  we  can  generally 
find  the  steps  which  fill  up  the  gap.  A  thoughtful 
comparison  of  the  phenomena  of  the  different  senses 
will,  we  believe,  reveal  these  steps.  We  repeat  here 
what  has  already  been  said  in  a  general  way  on  page 
13.  Commencing  with  the  lowest  of  the  specialized 
senses,  the  gustative,  an  impression  on  the  nerves  of 
taste  is  referred,  as  in  the  case  of  common  sensory 
fibers,  to  their  peripheral  extremity :  the  sensation  is 
on  the  tongue.  In  the  case  of  the  olfactive,  we  have  a 
sensation  still  at  the  peripheral  extremity,  i.  e.,  in  the 
nose,  but  also  a  reference  to  an  external  body  at  a  dis- 
tance as  its  cause.  Here  the  objective  cause  and  the 
subjective  sensation  are  separated,  and  both  distinct  in 
the  mind.  In  the  case  of  the  auditive  nerve,  the  sen- 
sation is  no  longer  perceived,  or  at  least  is  very  im- 
perfectly perceived,  in  the  ear,  but  is  nearly  wholly 
objective,  i.  e.,  referred  to  the  distant  sounding  body. 
Finally,  in  the  case  of  the  optic  nerve,  the  impression 
is  so  wholly  projected  outward  that  the  very  reminis- 
cence of  its  subjectivity  is  entirely  lost.  We  are  per- 
fectly unconscious  of  any  sensation  in  the  eye  at  all. 

Illustrations  of  this  Property.— We  will  now  try  to 
make  this  property  clear  by  many  illustrative  experi- 
ments. 

Experiment  1. — If  the  retina  or  the  optic  nerve  in 
any  portion  of  its  course  were  irritated  in  any  way,  by 
pinching,  by  scratching,  or  by  electricity,  we  should 
certainly  not  feel  any  pain  at  all,  but  see  a  flash  of  light. 
But  where  ?  Not  at  the  peripheral  extremity  only,  not 
in  the  eye,  but  beyond  in  the  field  of  mew.  Of  course. 


FUNCTION  OF  THE   RETINA.  67 

this  experiment  can  not  be  easily  made.  It  has  been 
made,  however,  by  passing  a  spark  of  electricity  through 
the  head  or  through  the  eye  in  such  wise  as  to  penetrate 
the  retina  or  traverse  the  optic  nerve.  The  phenom- 
enon has  also  been  observed  in  cases  of  extirpation  of 
the  eye  at  the  moment  of  section  of  the  optic  nerve. 
(Helmholtz.) 

Experiment  2.  Phosphenes. — Press  the  finger  into 
the  internal  corner  of  the  eye :  you  perceive  a  brilliant 
colored  spectrum  in  the  field  of  view  on  the  opposite  or 
external  side.  The  spectrum  thus  produced  has  a  deep 
steel-blue  center,  with  a  brilliant  yellow  border,  and 
reminds  one  of  the  beauty  spots  on  a  peacock's  feather 
or  a  butterfly's  wring.  Remove  the  pressure  to  any 
other  part,  and  the  spectrum  moves  also,  but  retains  its 
opposite  position  in  the  field  of  view.  In  this  familiar 
experiment  the  pressure  indents  the  sclerotic  and  causes 
a  change  or  irritation  on  the  forward  portion  of  the 
retina ;  and  any  change  whatever  on  the  retina  is  always 
referred  directly  outward  at  a  right  angle  to  the  point 
impressed,  and  therefore  to  the  opposite  side  of  the  field 
of  view.  These  colored  spectra  have  been  called  phos- 
phenes. 

Experiment  3.  Muscce  Volitantes. — If  we  gaze  on 
a  white  wall  or  ceiling,  or,  still  better,  on  a  bright  sky, 
we  see  indistinct  motes  floating  about  in  the  field  of 
view  on  the  wall  or  sky,  and  slowly  gravitating  down- 
ward. Sometimes  they  are  undulating,  transparent 
tubes,  with  nucleated  cells  within ;  sometimes  they  are 
like  inextricably  tangled  threads,  or  like  matted  masses 
of  spider's  web ;  sometimes  they  are  slightly  darker 
spots,  like  faint  clouds.  They  are  called  muscce  voli- 
tantes,  or  flying  gnats.  What  are  they  ?  They  are  specks 
or  imperfections  in  the  transparency  of  the  vitreous 


68  MONOCULAR  VISION. 

humor.  As  fishes  or  other  objects  floating  in  mid  water 
of  a  clear  lake  on  a  sunny  day  cast  their  shadows  on  the 
bottom  ooze,  even  so  these  motes  in  the  clear  medium 
of  the  vitreous  humor,  in  the  strong  light  of  the  sky, 
cast  their  shadows  on  the  retinal  bottom.  Now,  as 
already  said,  all  changes  in  the  retina,  of  whatever  kind, 
whether  produced  by  images,  or  shadows,  or  mechani- 
cal irritations,  are  projected  outward  into  the  field  of 
view,  and  appear  there  as  something  visible. 

Experiment  4-  Purkinjds  Figures.  —  Stand  in  a 
dark  room  with  a  lighted  candle  in  hand.  Shutting  the 
left,  hold  the  candle  very  near  the  right  eye,  within 
three  or  four  inches,  obliquely  outward  and  forward,  so 
that  the  light  shall  strongly  illuminate  the  retina.  Now 
move  the  light  about  gently,  upward,  downward,  back 

and  forth,  while  you  gaze  in- 

FIG.  21.  ,-,  ,,  ,, 

tently  on  the  wall  opposite. 
Presently  the  field  of  view  be- 
comes dark  from  the  intense 
impression  of  the  light,  and 
then,  as  you  move  the  light 
about,  there  appears  projected 
on  the  wall  and  covering  its 
whole  surface  a  shadowy,  ghost- 
like image,  like  a  branching, 


INTERNAL  VIEW  OF  THE    RETINA,    leaflegg      tree      Qr     }{^Q     a 
showing  the  retinal  vessels  rami-  • 

fying  over  the  surface,  but  avoid-    bodileSS       Spider       with        many 


cie  Jfd6)  C6ntral  SPOt'    (After  Branching  legs.     What   is  it  ? 
It    is   an   exact    but   enlarged 

image  of  the  blood-vessels  of  the  retina  (Fig.  21).  These 
come  in  at  the  entrance  of  the  optic  nerve,  ramify  in 
the  middle  layer,  and  therefore  in  the  strong  light  cast 
their  shadows  on  the  bacillary  layer,  of  the  retina.  The 
impression  of  these  shadows  is  projected  outward  into 


FUNCTION  OF  THE  RETINA.  09 

the  field  of  view,  and  seen  there  as  an  enlarged  shad- 
owy image.  These  have  been  called  Purkinje's  figures, 
from  the  discoverer. 

Experiment  5.  Ocular  Spectra. — Look  a  moment 
steadily  at  the  setting  sun,  and  then,  turning  away  the 
eye,  look  elsewhere — at  the  sky,  the  ground,  the  wall :  a 
vivid  colored  spectrum  of  the  sun  (or  many  of  them,  if 
the  eye  has  not  been  steady  while  regarding  the  sun)  is 
projected  into  the  field  of  view,  and  follows  all  the 
motions  of  the  eye.  This  spectrum,  on  a  bright  ground, 
like  the  sky,  to  my  eye  is  first  green,  then  blue,  then 
purple,  and  so  gradually  fades  away.  The  spectrum  is 
equally  seen  wrhen  the  eye  is  shut ;  but  then,  being  pro- 
jected on  a  dark  ground,  the  color  is  apt  to  be  comple- 
mentary to  that  of  the  same  spectrum  seen  against  the 
bright  ground  of  the  sky.  It  is  first  blue,  then  yellow, 
then  green,  and  so  fades.  The  explanation  is  obvious. 
The  strong  impression  of  the  image  of  the  sun  on  the 
retina  induces  a  change  which  lasts  some  time ;  but 
every  change  in  the  retina  appears,  by  projection,  in 
the  field  of  view. 

This  experiment  may  be  made  in  an  infinite  variety 
of  ways.  If  at  night  we  gaze  steadily  at  a  candle-  or 
lamp-flame,  or  flame  of  any  kind,  and  then  turn  away 
and  look  at  the  wall,  we  see  a  vivid  colored  spectrum 
of  the  flame,  which  gradually  changes  its  color  and 
fades  away.  In  my  own  case,  on  shutting  the  eyes, 
the  spectrum  is  first  bright  yellow,  with  deep-red  border 
and  dark  olive-green  corona ;  then  it  becomes  greenish- 
yellow,  and  then  green  with  red  border,  then  red  with 
indigo  border,  and  so  fades  away.  With  the  eyes  open 
the  changes  are  slightly  different,  and  in  some  stages 
are  complementary  to  the  preceding.  Again,  if  we 
look  a  moment  through  a  window  at  a  bright  sky,  and 


70  MONOCULAR  VISION. 

then  quickly  turn  the  eye  to  the  wall,  we  will  see  a 
faint  spectrum  of  the  window  with  all  its  bars  projected 
against  the  wall.  If  we  look  intently  and  steadily  at 
any  object  strongly  differentiated  from  the  rest  of  the 
wall  of  a  room,  as  a  small  picture-frame  or  a  clock, 
then  look  to  some  other  part  of  the  wall,  the  spectrum 
of  the  object  will  be  seen  on  the  wall  and  follow  the 
eye  in  its  motions.  This  experiment  succeeds  best  when 
we  are  just  waked  up  in  the  morning,  and  while  the 
retina  is  still  sensitive  from  long  rest. 

The  experiment  may  be  varied  thus :  Lay  a  small 
patch  of  vermilion  red — such  as  a  red  wafer — on  a 
white  sheet  of  paper,  and  gaze  steadily  at  it  in  a  strong 
light  for  a  considerable  time,  and  then  turn  the  eye 
to  some  other  part  of  the  paper.  A  spectrum  of  the 
wafer  will  be  seen,  because  every  difference  in  the 
retina  will  appear  as  a  corresponding  difference  in  the 
field.  It  will  be  observed,  also,  that  the  spectrum  will 
be  bluish-green,  i.  e.,  complementary  to  the  red  of  the 
object.  The  reason  seems  to  be  that  the  long  impres- 
sion of  the  red  produces  a  prof ounder  change,  or  fatigue, 
in  those  rods  or  cones,  or  those  portions  of  the  cones, 
which  co-vibrate  with  red ;  therefore,  when  we  look 
elsewhere,  of  the  different  colors  which  make  up  white 
light,  the  retina  is  least  sensitive  to  red,  and  therefore 
the  other  rays  will  predominate.  Now  these  other  rays, 
which  with  red  make  up  white  light,  are  what  are  called 
complementary  to  red.  A  mixture  of  these  makes  a 
bluish-green.  It  is  difficult,  however,  to  account  for  all 
the  phenomena  of  the  colors  of  spectra  by  this  "  law 
of  fatigue" 

Complementary  spectra  may  be  still  more  beauti- 
fully seen  by  gazing  on  the  brilliant  contrasted  colors 
of  a  stained-glass  window,  and  then  turning  the  eyes 


FUNCTION  OF   THE  RETINA.  f  1 

on  a  white  wall.  The  whole  pattern  of  the  window 
will  be  distinctly  seen  in  complementary  colors. 

Let  it  be  observed  here  how  differently  spectral 
images  behave  from  objects.  When  we  move  the  eyes 
about,  the  images  of  objects  move  about  on  the  retina, 
but  the  objects  seem  to  remain  unmoved.  Spectral 
impressions  on  the  retina,  on  the  contrary,  remain  in 
the  same  place,  and  therefore  their  external  images  fol- 
low the  motions  of  the  eye. 

We  are  now  prepared  to  generalize  from  these  ob- 
servations. It  is  evident  that  what  we  call  the  field  of 
view  is  naught  else  than  the  external  projection  into 
space  of  retinal  states.  All  variations  of  state  of  the 
one,  whether  they  be  images,  or  shadows,  or  mechanical 
irritation,  whether  they  be  normal  or  abnormal,  are 
faithfully  reproduced  as  corresponding  variations  of 
appearances  in  the  other.  This  sense  of  an  external 
visual  h'eld  is  ineradicable.  If  we  shut  our  eyes,  still 
the  field  is  there,  and  still  it  represents  the  state  of  tho 
retina.  With  the  eyes  open,  we  call  it  the  field  of  view, 
filled  with  objects ;  with  the  eyes  shut,  it  is  the  field 
of  darkness — visible,  palpable  darkness,  without  visible 
objects.  The  one  is  the  outward  projection  of  the 
active  state  of  the  retina,  crowded  with  its  retinal 
images ;  the  other  is  the  outward  projection  of  the 
comparatively  passive  state  of  the  retina,  without  defi- 
nite images.  When  we  shut  our  eyes,  or  stand  with 
eyes  open  in  a  perfectly  dark  room,  the  field  of  dark- 
ness is  an  actual  visible  field,  tho  outlines  of  which  we 
can,  at  least  imperfectly,  mark  out.  It  is  wholly  differ- 
ent from  a  simple  absence  of  visual  impression.  We 
see  a  dark  field  in  front,  but  nothing  at  all  behind  the 
head.  The  dark  field  is  also  quite  different  from  black- 
ness. If  we  must  describe  it  as  of  any  color,  we  should 
4 


72  MONOCULAR  VISION. 

say  that  it  is  a  dark  grayish  or  brownish  field,  full  of 
irregular,  confused,  and  ever-shifting  lines  and  cloud- 
ings.  If  the  retina  has  been  previously  strongly  im- 
pressed, spectra  are  seen  on  this  dark  background  when 
the  eyes  are  shut.  When  the  eyes  are  open,  the  same 
spectra  are  seen  on  the  bright  ground  of  the  sky  or  wall, 
and  the  difference  of  the  background  makes  the  differ- 
ence of  the  color  of  the  spectra  in  the  two  cases. 

Now  the  same  inherent  activity  of  the  retina  which 
produces  the  sense  of  a  dark  field  with  its  confused  mark- 
ings and  cloudings,  will  also,  under  certain  circumstances 
of  peculiar  sensitiveness  of  the  retina,  as  after  complete 
rest  in  the  early  morning,  give  rise  spontaneously  to 
more  definite  spectra,  often  of  beautiful  colors.  I  have 
often,  in  bed  in  the  morning,  watched  with  eyes  shut 
these  splendid  spectra,  consisting  of  a  colored  patch 
surrounded  with  a  border  of  complementary  color,  ea3h 
color  closing  in  on  the  center  and  so  vanishing,  while 
another  border  commences  on  the  outside  to  close  in  in 
the  same  way.  Thus,  just  as  impressions  or  images 
made  normally  on  the  retina  by  actual  objects  from 
without  are  projected  into  the  field  of  view  and  seen 
there  as  the  true  signs  of  objects,  even  so  impressions 
made  on  the  retina  abnormally  from  within,  by  the 
mind  or  imagination,  are  also  sometimes  projected  out- 
ward, and  become  the  delusive  signs  of  external  ob- 
jects having  no  existence.  It  is  thus  that  the  diseased 
brain  gives  rise  to  delusive  visual  phenomena. . 

Corresponding  Points,  Retinal  and  Spatial.— Further, 
it  is  evident  that  every  point — every  rod  or  cone — in 
the  retina  has  its  invariable  correspondent  in  the  visual 
field,  and  vice  versa.  Moreover,  since  the  central  ray  of 
the  pencil  of  every  radiant  point  in  the  external  world 
passes  through  the  nodal  point  of  the  crystalline  lens, 


FUNCTION  OF  THE  RETINA. 


it  is  evident  that  these  lines  must 
In  other  words,  the  lines  forming  coi 
in  space  and  on  the  retina  cross  each  other  m" 
point,  and  therefore  the  positions  of  these  correspondent 
points,  external  and  internal,  are  completely  reversed. 
Thus  not  only  are  the  retinal  images  inverted,  but  the 
relative  positions  of  these  images  are  inverted,  and  the 
position  of  every  focal  point  is  the  inverse  of  its  corre- 
spondent radiant  point.  It  is  obvious,  then,  that  the 
left  half  of  the  retina  corresponds  with  the  right  half 
of  the  field  of  view,  and  the  right  half  of  the  former  to 
the  left  half  of  the  latter  ;  and  so  also  the  upper  half  of 
the  former  corresponds  to  the  lower  half  of  the  latter, 
and  the  lower  half  of  the  former  to  the  upper  half  of 
the  latter. 

There  are  some  peculiarities  of  vision  which  we  are 
now  prepared  to  explain. 

'l.  Properties  of  the  Central  Spot,  and  of  its  Represen- 
tative in  the  Visual  Field.  —  We  have  already  stated  that 
there  are  two  spots  on  the  retina  where  the  constituent 
layers  do  not  all  exist.  The  central  spot  is  destitute  of 
all  except  the  bacillary  layer  ;  the  blind  spot,  of  all  ex- 
cept the  fibrous  layer. 

The  central  spot  (macula  centralis)  is  a  small  de- 
pression not  more  than  one  thirtieth  of  an  inch  in  diam- 
eter, situated  directly  in  the  axis  of  the  eye,  or  what 
might  be  called  the  south  pole  of  this  globe.  It  differs 
from  other  parts  of  the  retina  (a)  by  wanting  the  fibrous 
and  granular  layers  ;  therefore  the  retina  is  much  thin- 
ner there,  and  the  spot  is  consequently  pit-shaped,  and  on 
this  account  is  often  called  the  fovea  centralis,  or  central 
pit.  Of  course,  the  absence  of  other  layers  exposes  the 
bacillary  layer  here  to  the  direct  action  of  light.  It  dif- 
fers again  (5)  by  the  presence  of  a  pale-yellow  coloring 


74:  MONOCULAR  VISION. 

matter  in  the  retinal  substance ;  hence  it  is  sometimes 
called  macula  lutea — the  yellow  spot.  It  differs,  again, 
(c)  in  a  finer  organization  than  any  other  part  of  the 
retina.  The  bacillary  layer  here  consists  only  of  cones, 
and  these  are  far  smaller,  and  therefore  more  numerous, 
than  elsewhere ;  being  here,  as  already  seen  (page  58), 
only  YTj-for  °^  an  mcn  m  diameter. 

Function  of  the  Central  Spot. — Every  point  on  the  reti- 
na, as  already  seen,  has  its  correspondent  or  representa- 
tive in  the  field  of  view.  Now  what  is  the  representative 
of  the  central  spot  ?  It  is  evidently  the  point,  or  rather 
the  line,  of  sight.  From  its  position  in  the  axis  of  the 
eye,  it  is  evident  that  on  it  must  fall  the  image  of  the 
object  or  part  of  the  object  looked  at,  or  of  all  points 
in  the  visual  line  or  line  of  sight.  Now,  if  we  look 
steadily  and  attentively  on  any  spot  on  the  wall,  and, 
without  moving  the  eyes,  observe  the  gradation  of  dis- 
tinctness over  the  field,  we  find  that  the  distinctness  is 
most  perfect  at  the  point  of  sight  and  a  very  small 
area  about  that  point,  and  becomes  less  and  less  as  we 
pass  outward  in  any  direction  toward  the  margins  of 
the  field  of  view.  Standing  two  feet  from  the  wall,  I 
look  at  my  pen  held  at  arm's  length  against  the  wall, 
and  of  course  see  the  pen  distinctly.  Looking  still  at 
the  same  spot,  I  move  the  pen  to  one  side  eight  or  ten 
inches :  I  now  no  longer  see  the  hole  in  the  back  of  the 
pen.  I  move  it  two  feet  or  more  to  one  side :  I  now 
no  longer  see  the  shape  of  the  pen.  I  see  an  elongated 
object  of  some  kind,  but  can  not  recognize  it  as  a  pen 
without  turning  my  eyes  and  bringing  its  image  on  the 
central  spot.  Hence,  to  see  distinctly  a  wide  field,  as 
in  looking  at  a  landscape  or  a  picture,  we  unconsciously 
and  rapidly  sweep  the  line  of  sight  over  every  part,  and 
then  gather  up  the  combined  impression  in  the  memory. 


FUNCTION  OF  THE  RETINA.  75 

Now  the  point  of  sight  with  a  very  small  area  about 
it  corresponds  to  the  central  spot,  and  the  margins  of 
the  field  of  view  correspond  to  the  extreme  forward 
margin  of  the  retina.  Therefore  the  organization  of 
the  retina  for  distinct  perception  is  most  perfect  in  the 
central  spot,  and  becomes  gradually  less  and  less  perfect 
as  we  pass  toward  the  anterior  margin,  where  its  per- 
ception is  so  imperfect  that  we  can  not  tell  exactly 
where  the  field  of  view  ends,  except  where  it  is  limited 
by  some  portion  of  the  face. 

Now  what  is  the  use  of  this  arrangement?  Why 
would  it  not  be  much  better  to  see  equally  distinctly 
over  all  portions  of  the  field  of  view  ?  I  believe  that 
the  existence  of  the  central  spot  is  necessary  to  fixed, 
thoughtful  attention,  and  this  again  in  its  turn  is  neces- 
sary for  the  development  of  the  higher  faculties  of  the 
mind.  In  passing  down  the  animal  scale,  the  central 
spot  is  quickly  lost.  It  exists  only  in  man  and  the 
',  higher  monkeys.  In  the  lower  animals,  it  is  necessary 
'for  safety  that  they  should  see  well  over  a  very  wide 
field.  In  man,  on  the  contrary,  it  is  much  more  neces- 
sary that  he  should  be  able  to  fix  undivided  attention  on 
the  thing  looked  at.  This  would  obviously  be  impos- 
sible if  other  things  were  seen  with  equal  distinctness. 
This  subject  is  more  fully  treated  in  the  final  chapter 
of  this  work. 

It  is  evident,  then,  that  distinctness  of  vision  is  a 
product  of  two  factors,  viz. :  1st,  an  optical  apparatus  for 
distinct  image  on  the  retina ;  and  2d,  a  retinal  organiza- 
tion for  distinct  perception  of  the  image  thus  formed. 
These  two  factors  are  perfectly  independent  of  each 
other.  If  I  hold  up  my  pen  before  my  eye,  but  very 
near,  and  then  look  at  the  sky,  the  outlines  of  the  pen 
are  blurred  because  the  retinal  image  is  so,  but  my  per- 


Y6  MONOCULAR  VISION. 

ception  is  perfect.  I  can  observe  with  great  accuracy 
the  exact  degree  of  indistinctness.  But  if  I  hold  the 
pen  far  to  one  side,  say  90°,  from  the  line  of  sight — on 
the  extreme  verge  of  the  field  of  view — it  is  again  in- 
distinct, much  more  so  than  before,  but  from  an  entirely 
different  cause,  viz.,  imperfect  perception  of  the  retinal 
image.  In  fact,  my  perception  is  so  imperfect  that  I 
can  not  tell  whether  the  image  is  perfect  or  not.  Thus 
there  are  two  forms  of  indistinctness  of  vision,  viz., 
indistinctness  from  imperfect  retinal  image,  and  indis- 
tinctness from  imperfect  retinal  perception.  The  for- 
mer is  an  effect  of  the  optical  instrument,  the  latter  of 
the  organization  of  the  sensitive  plate. 

It  is  evident  from  the  above  that  an  elaborate 
structure  of  the  lens,  for  making  very  exact  images  of 
objects  on  the  margins  of  the  field  of  view,  would  be  of 
no  use  to  man  for  want  of  corresponding  distinctness 
of  perception  in  the  anterior  margins  of  the  retina. 
Therefore,  as  already  stated  on  page  37,  the  peculiar 
structure  of  the  crystalline,  viz.,  its  increasing  density 
to  the  center,  is  of  use  to  man  only  as  correcting  aber- 
ration, and  not  in  conferring  the  faculty  of  periscopism. 
In  the  lower  animals,  however,  in  which  periscopism  is 
so  important,  this  structure  of  the  lens  subserves  both 
purposes.  So  far  as  this  property  is  concerned,  there- 
fore, the  structure  in  man  may  be  regarded  as  having 
outlived  its  use. 

Minimum  Visibile. — Is  there  a  limit  to  the  small- 
ness  of  a  visible  point  ?  This  question  has  been  dis- 
cussed by  metaphysicians.  But,  as  usually  understood 
by  them,  there  is  no  such  thing  as  a  minimum  visibile. 
There  is  no  point  so  small  that  it  can  not  be  seen  if 
there  be  light  enough.  For  example  :  a  fixed  star  may 
be  magnified  10  diameters,  100  diameters,  1,000  diam- 


FUNCTION  OF  THE  RETINA.  77 

eters,  5,000  diameters,  and  still  it  is  to  us  a  mathemati- 
cal point  without  dimensions.  How  much  more,  there- 
fore, is  it  without  dimensions  to  the  naked  eye !  And 
yet  it  is  perfectly  visible.  The  only  sense  in  which 
science  recognizes  a  minimum  visibile  is  the  smallest 
space  or  object  which  can  ~be  seen  as  a  surface  or  as  a 
magnitude — the  smallest  distance  within  which  two 
points  or  two  lines  may  approach  each  other  and  yet  be 
perceived  as  two  points  or  two  lines.  In  this  sense  it 
is  a  legitimate  inquiry ;  for  there  is  here  a  real  limit, 
which  depends  on  the  perfection  of  the  eye  as  an  in- 
strument and  the  fineness  of  the  organization  of  the 
retina. 

We  can  best  make  this  point  clear  by  showing  a 
similar  property,  but  far  less  perfect,  in  the  lower  sense 
of  touch.  There  is  also  a  minimum  tactile. 

Experiment.  —  Take  a  pair  of  dividers ;  stick  on 
each  point  a  mustard-seed  shot,  so  that  the  impression 
on  the  skin  shall  not  be  too  pungent.  Now  try,  on 
another  person  whose  eyes  are  shut,  the  least  distance 
apart  at  which  two  distinct  impressions  can  be  per- 
ceived. It  will  be  found  that,  on  the  middle  of  the 
back,  it  is  about  3  inches ;  on  the  arm  or  back  of  the 
hand,  it  is  about  i  to  f  inch;  on  the  palm,  about  J 
inch ;  on  the  finger-tips,  about  -^  or  -fa  inch ;  and  on 
the  tip  of  the  tongue,  about  -fa  inch,  or  less. 

Now,  sight  is  a  very  refined  tact,  and  the  retina  is 
specially  organized  for  an  extreme  minimum  tactile. 
There  is  no  doubt  that  the  size  of  the  cones  of  the  cen- 
tral spot  determines  the  minimum  visibile.  If  the 
images  of  two  points  fall  on  the  same  retinal  cone,  they 
will  make  but  one  impression,  land  therefore  be  seen  as 
one ;  but  if  they  are  far  enough  apart  to  impress  two 
cones,  then  they  will  be  seen  as  two  points.  So  also 


78  MONOCULAR  VISION. 

of  an  object  :  if  its  image  on  the  retina  be  sufficient  to 
cover  two  or  more  cones  of  the  central  spot,  then  it 
will  be  seen  as  a  magnitude.  Taking  the  diameter  of 
central-spot  cones  to  be  TTFVo  (which  is  the  diameter 
given  by  some),  the  smallest  distance  between  two 
points  which  ought  to  be  visible  at  five  inches  dis- 
tance is  Y^Vo"  °^  an  incn-  This  is  found  to  be  about 
the  fact  in  good  eyes. 

2.  Blind  Spot.  —  This  is  the  spot  where  the  optic  nerve 
enters  the  ball  of  the  eye.  Objects  whose  images  fall 
on  this  spot  are  wholly  invisible.  It  is  for  this  reason 
that  the  point  of  entrance  is  always  placed  out  of  the 
axis,  about  ^  inch  on  the  nasal  side.  For,  if  it  were  in 
the  axis,  of  course  the  image  of  the  object  we  looked 
at  would  fall  on  this  spot,  and  the  object  would  conse- 
quently disappear  from  view.  The  structural  cause  of 
the  blindness  of  this  spot  we  have  already  explained  on 
page  59.  It  is  the  absence  of  the  bacillary  layer.  The 
existence  of  the  blind  spot  may  be  easily  proved  by 
experiments  which  any  one  can  repeat. 

Experiment  1.  —  Make  two  conspicuous  marks,  A  and 
B,  a  few  inches  apart.  Then  shut  the  left  eye,  and 


while  looking  steadily  with  the  right  eye  at  the  left 
object,  Ay  bring  the  paper  gradually  nearer  and  nearer  : 
at  a  certain  point  of  approach  B  will  disappear  utterly. 
Continue  to  bring  the  paper  nearer,  still  looking  steadily 
at  A;  at  a  certain  nearer  point  B  will  reappear.  The 
explanation  is  as  follows  :  At  first,  when  the  paper  is  at 
considerable  distance,  say  18  inches,  the  image  of  A  is, 
of  course,  on  the  central  spot,  for  the  axis  of  the  eye  is 
directed  toward  this  point  ;  but  the  image  of  B  falls  a 
little  to  the  internal  or  nasal  side  of  the  central  spot, 


FUNCTION  OF  THE  RETINA. 


FIG.  25. 


B 


viz.,  between  the  central  spot  and  the  blind  spot.  Now, 
as  the  paper  comes  nearer,  the  eye  turns  more  and  more 
in  order  to  regard  A,  the  image  of  B  travels  slowly  over 
the  retina  noseward  until  it 
reaches  the  blind  spot,  and  the 
object  disappears.  As  the  pa- 
per still  approaches,  the  image 
of  B  continues  to  travel  in  the 
same  direction  until  it  crosses 
over  the  blind  spot  to  the  other 
side,  when  the  object  immedi- 
ately reappears. 

The  accompanying  diagram, 
Fig.  25,  illustrates  this  phe- 
nomenon. Let  A  and  B  rep- 
resent the  two  objects,  and  R 
and  L  the  positions  of  the  right 
and  left  eyes  respectively.  The 
right  is  drawn,  but  the  left, 
being  shut,  is  not  drawn,  but 
only  its  position  indicated  by  the 
dot.  The  central  spot  is  repre- 
sented by  £,  in  the  axis  A  c, 
and  the  blind  spot  by  0,  where 
the  optic  nerve  enters.  It  is 
obvious  that  the  image  a  of  the 
object  A  will  be  always  on  <?, 
and  the  place  of  the  image  of 
B  is  on  the  intersection  J  of 
the  line  B  ft  with  the  retina. 
Now,  as  the  eye  approaches  the  objects  A  and  B,  it  is 
seen  that  the  image  I  of  B  travels  toward  the  blind 
spot,  o.  At  the  second  position  of  the  eye,  R',  it  has 
not  reached  it.  At  the  third  position,  E"^  it  is  upon  it. 


80  MONOCULAR  VISION. 

At  the  fourth  position,  7?'",  it  has  already  crossed  over 
and  is  now  on  the  other  side.  At  the  third  position, 
R' ',  the  object  B  disappears  from  view. 

The  distance  at  which  the  disappearance  takes  place 
will,  of  course,  depend  on  the  distance  between  the 
objects  A  and  B.  If  these  are  3  inches  apart,  then 
the  disappearance  on  approach  from  a  greater  distance 
takes  place  at  about  1  foot,  and  the  reappearance  at 
about  10  inches.  If  the  objects  be  1  foot  apart,  then 
the  disappearance  takes  place  at  48  inches,  and  the  reap- 
pearance at  38  inches. 

Experiment  2. — Place  a  small  piece  of  money  on 
the  table.  Shutting  the  left  eye,  look  steadily  with  the 
right  at  a  spot  on  the  table  a  little  to  the  left  of  the 
piece,  and  move  the  piece  slowly  to  the  right  while  the 
point  of  sight  remains  fixed ;  or  else,  the  piece  of  money 
remaining  stationary,  move  the  point  of  sight  slowly  to 
the  left.  At  a  certain  distance  from  the  point  of  sight 
the  piece  will  disappear  from  view.  Beyond  this  dis- 
tance it  will  reappear. 

Experiment  3. — The  experiment  may  be  varied  in 
many  ways.  If,  when  the  object  B  has  disappeared 
from  view  in  the  previous  experiments,  we  open  the 
left  eye  and  shut  the  right,  and  look  across  the  nose  at 
the  object  B,  then  A  will  disappear.  Thus  we  may 
make  them  disappear  alternately.  If,  finally,  we  squint 
or  cross  the  eyes  in  such  wise  that  the  right  eye  shall 
look  at  the  left  object  A,  and  the  left  eye  at  the  right 
object  B  (the  two,  A  and  B,  had  best  be  similar  in 
this  case),  then  B  will  fall  on  the  blind  spot  of  the  right 
eye  and  A  on  the  blind  spot  of  the  left  eye,  and  they 
will  both  disappear;  but  a  combined  image  of  A  and 
B  on  the  central  spots  of  the  two  eyes  will  be  seen  in 
the  middle.  This,  however,  is  a  phenomenon  of  bin- 


FUNCTION  OF  THE   RETINA.  81 

ocular  vision,  and  will  be   explained  farther  on  (see 
page  107). 

Experiment  4- — Any  object,  if  not  too  large,  may 
be  made  to  disappear  by  causing  its  image  to  fall  on 
the  blind  spot.  For  example :  From  where  I  now  sit 
writing  the  door  is  distant  about  10  feet.  I  shut  my 
left  eye  and  look  at  the  door-knob.  I  now  slowly  re- 
move the  point  of  sight  and  make  it  travel  to  the  left, 
but  at  the  same  level;  when  it  reaches  about  3  feet  to 
the  left,  the  door-knob  disappears ;  when  it  reaches  4 
feet,  it  reappears.  Precisely  in  the  same  way  a  bright 
star  or  planet,  like  Yen  us  or  Jupiter,  or  even  the 
moon,  may  be  made  to  disappear  completely  from 
sight. 

Size  of  the  Blind  Spot.— As  every  point  in  the  retina 
has  its  representative  in  the  visual  field,  it  is  evident 
that  the  size  of  the  invisible  spot  is  determined  by  the 
size  of  the  blind  retinal  spot.  We  may,  therefore,  I 
measure  the  latter  by  the  former.  I  have  made  many  \ 
experiments  to  determine  the  size  of  the  invisible  spot. 
At  the  distance  of  3J  feet  (42  inches)  I  find  the  invisi- 
ble spot  12  inches  from  the  point  of  sight,  and  3J  inches 
in  diameter ;  i.  e.,  a  circle  of  3J  inches  will  entirely  dis- 
appear at  that  distance.  Taking  the  nodal  point  of  the 
lenses  or  the  point  of  ray-crossing  at  f  of  an  inch  in  front 
of  the  retina  (it  is  a  very  little  less),  an  invisible  spot  of 
3£  inches  at  a  distance  of  3£  feet  would  require  a  blind 
retinal  spot  of  a  little  more  than  -fa  inch  in  diameter. 
At  36  feet  distance  the  invisible  area  would  be  3  feet ; 
it  would  cover  a  man  sitting  on  the  ground.  At  100 
yards  distance  the  invisible  area  would  cover  a  circle  of 
8  feet  diameter.  In  a  word,  the  angular  diameter  of 
the  invisible  spot  is  a  little  more  than  4f  °.  Helmholtz 
makes  it  a  little  larger  than  this. 


82  MONOCULAR  VISION. 

Representative  in  the  Visual  Field  of  the  Blind  Spot. — 
Since  every  condition  of  the  retina  has  its  visible  repre- 
sentative in  the  field  of  view,  it  may  be  asked,  "  If  there 
be  a  blind  spot,  why  do  we  not  see  it,  when  we  look  at 
a  white  wall  or  bright  sky,  as  a  black  spot,  or  a  dusky 
or  dim  spot,  or  a  peculiar  spot  of  some  kind  ? "  I  an- 
swer :  1.  With  both  eyes  open  there  are,  of  course,  two 
fields  of  view  partly  overlapping  each  other.  Now  the 
invisible  spots  in  these  two  fields  do  not  correspond, 
and  therefore  objects  in  the  invisible  spot  of  one  eye 
are  seen  perfectly  by  the  other  eye,  and  hence  there 
is  no  invisible  area  for  the  binocular  observer.  But  it 
will  be  objected  that  even  with  one  eye  we  see  no  pecu- 
liar spot  on  a  white  wall.  I  therefore  add :  2.  That  we 
see  distinctly  only  a  very  small  area  about  the  point  of 
sight,  and  distinctness  decreases  rapidly  in  going  from 
this  point  in  any  direction.  Therefore  the  correspon- 
dent or  representative  in  the  field  of  view  may  well  be 
overlooked,  unless  it  be  conspicuous,  i.  e.,  strongly  dif-" 
ferentiated  from  the  rest  of  the  general  field.  3,  But  if 
this  were  all,  close  observation  would  certainly  detect  it. 
The  true  reason  is  very  different,  and  the  explanation  is 
to  be  sought  in  an  entirely  different  direction.  Writers 
on  this  subject  have  expected  to  find  a  visible  representa- 
tive, and  have  sought  diligently  but  in  vain  for  it.  But 
the  fact  is,  they  ought  not  to  have  expected  to  find  it. 
The  expectation  is  an  evidence  of  confusion  of  thought 
— of  confounding  blackness  or  darkness  with  absence  of 
visual  activity.  Blackness  or  darkness  is  itself  but  the 
outward  projection  of  the  unimpressed  state  of  the  bacil- 
lary  layer ;  but  there  is  no  bacillary  layer  here.  We 
might  as  well  expect  to  see  a  dark  spot  with  our  fingers 
as  in  the  representative  of  the  blind  spot.  A  black 
spot,  or  a  dark  spot,  or  a  visible  spot  of  any  kind,  is 


FUNCTION   OF  THE   RETINA.  83 

not  the  representative  in  space  of  a  blind  or  insensitive 
retinal  spot.  The  true  representative  of  a  blind  spot 
is  simply  an  invisible  spot,  or,  in  other  words,  a  spot  in 

which  objects  are  not  seen.     If  we  could  differentiate  it 
«/ 

in  any  way,  it  would  be  visible,  which  it  is  not.  As  it 
can  not  be  differentiated  in  any  way,  the  mind  seems 
to  extend  the  general  ground  color  of  the  neighboring 
field  of  view  over  it.  This  is,  however,  a  psychological 
rather  than  a  visual  phenomenon.  It  is  for  a  similar 
reason  that  it  is  impossible  to  see  any  limit  to  the  field 
of  view,  except  where  it  is  limited  by  the  parts  of  the 
face,  as  nose,  brows,  etc.  There  is  a  certain  limit  hori- 
zontally outward  where  vision  ceases,  but  it  is  impos- 
sible to  detect  any  line  of  demarkation  between  the 
visible  and  the  invisible. 

3.  Erect  Vision. — Retinal  images  are  all  inverted. 
External  images  or  signs  of  objects  are  outward  projec- 
tions of  retinal  images.  How,  then,  with  inverted  retinal 
images,  do  we  see  objects  in  their  right  position,  i.  e., 
erect  f  This  question  has  puzzled  metaphysicians,  and 
many  answers  characteristic  of  this  class  of  philosophers 
have  been  given.  The  true  scientific  answer  is  found 
in  what  is  called  the  "  law  of  visible  direction"  This 
law  may  be  thus  stated  :  When  the  rays  from  any  radi- 
ant strike  the  retina,  the  impression  is  referred  ~back  jy  p 
along  the  ray-line  (central  ray  of  the  pencil)  into  space, 
and  therefore  to  its  proper  place.  For  example  :  The 
rays  from  a  star  (which  is  a  mere  radiant  point)  on  the 
extreme  verge  of  the  field  of  view  to  the  right  enter 
the  eye  and  strike  the  retina  on  its  extreme  anterior 
left  margin ;  the  impression  is  referred  straight  back 
along  the  ray-line,  and  therefore  seen  in  its  proper  place 
on  the  right.  A  star  on  the  left  sends  its  rays  into 
the  eye  and  strikes  the  right  side  of  the  retina,  and  the 


84:  MONOCULAR  VISION. 

impression  is  referred  back  along  the  ray-line  to  its  ap- 
propriate place  on  the  left.  So  also  points  or  stars 
above  the  horizon  in  front  impress  the  lower  portion 
of  the  retina,  and  the  impression  is  referred  back  at 
right  angles,  or  nearly  at  right  angles,  to  the  impressed 
surface,  and  therefore  upward;  and  radiants  below  the 
horizon,  on  the  ground,  impress  the  upper  half  of  the 
retina  and  are  referred  downward. 

Comparison  with  Other  Senses. — There  is  nothing 
absolutely  peculiar  in  this ;  but  only  a  general  property 
of  sense  refined  to  the  last  degree  in  the  case  of  sight, 
owing  to  the  peculiar  and  exquisite  structure  of  the 
bacillary  layer  of  the  retina.  For  example :  Suppose, 
standing  with  our  eyes  bandaged,  any  one  should  with 
a  rod  push  against  our  body.  We  immediately  infer 
the  direction  of  the  external  rod  by  the  direction  of 
the  push.  Or  another  example  :  Suppose  we  stood 
naked  in  a  pond  of  placid  water,  with  eyes  bandaged, 
and  some  one  on  shore  agitated  the  water ;  the  advanc- 
ing waves  would  after  a  while  reach  us  and  tap  gently 
upon  the  sensitive  skin.  Could  we  not  infer  the  direc- 
tion of  the  distant  cause  from  the  direction  of  the 
blows  ?  Is  it  any  wonder,  then,  that  when  the  rays  of 
light  crossing  one  another  in  the  nodal  point  punch 
against  the  interior  hollow  of  the  retina,  we  should 
infer  the  direction  of  the  cause  by  the  direction  of  the 
punch ;  i.  e.,  that  we  should  refer  each  radiant  back  to 
its  proper  place  in  space  ? 

Thus  it  is  seen  that  it  is  in  no  wise  contrary  to  the 
general  law  of  the  senses,  that  we  should  refer  single 
radiants,  like  stars,  back  to  their  proper  place  in  space 
and  see  them  there.  But  objects  are  nothing  else  than 
millions  of  radiants,  each  with  its  own  correspondent 
focal  point  in  the  retinal  image.  Each  focal  impression 


FUNCTION  OF  THE  RETINA.  85 

is  referred  back  to  its  correspondent  radiant,  and  thus 
the  external  image  is  reconstructed  in  space  in  its  true 
position,  or  is  rein  verted  in  the  act  of  projection. 

Law  of  Visible  Direction. — After  these  illustrations 
and  explanations  we  return  to  the  law,  and  restate  it 
thus :  Every  impression  on  the  retina  reaching  it  by  a 
ray-line  passing  through  the  nodal  point  is  referred 
back  along  the  same  ray-line  to  its  true  place  in  space. 
Thus,  for  every  radiant  point  in  the  object  there  is  a 
correspondent  focal  point  in  the  retinal  image ;  and 
every  focal  point  is  referred  back  along  its  ray-line  to 
its  own  radiant,  and  thus  the  external  image  (object) 
is  reconstructed  in  its  proper  position.  Or  it  may  be 
otherwise  expressed  thus:  Space  in  front  of  us  is 
under  all  circumstances  the  outward  projection  of  ret- 
inal states.  With  the  eyes  open,  the  field  of  view  is 
the  outward  projection  of  the  active  or  stimulated  state 
of  the  retina ;  with  the  eyes  shut,  the  field  of  darkness 
is  the  outward  projection  of'  the  unstim.ulated  or  pas- 
sive state  of  the  retina.  Thus  the  internal  retinal  con- 
cave with  all  its  states  is  projected  outward,  and  becomes 
the  external  spatial  concave,  and  the  two  correspond, 
point  for  point.  Now  the  lines  connecting  the  corre- 
sponding points,  external  and  internal,  cross  each  other 
at  the  nodal  point,  and  impressions  reach  the  retina  and 
are  referred  back  into  space  along  these  lines;  or,  in 
other  words,  these  corresponding  points,  spatial  and 
retinal,  exchange  with  each  other  by  impression  and 
external  projection.  This  would  give  the  true  position 
of  all  objects  and  of  all  radiants,  and  therefore  com- 
pletely explains  erect  vision  with  inverted  retinal  image. 

We  see,  then,  that  the  sense  of  sight  is  not  excep- 
tional in  this  property  of  direction -reference.  But 
what  is  exceptional  is  the  marvelous  perfection  of  this 


86  MONOCULAR  VISION. 

property — the  mathematical  accuracy  of  its  perception 
of  direction.  This  is  the  result  partly  of  the  remark- 
able structure  of  the  bacillary  layer.  Every  rod  and 
cone  has  its  own  correspondent  in  space,  and  the  ex- 
treme minuteness  and  therefore  number  of  separably 
discernible  points  in  space  are  measured  by  the  mi- 
nuteness and  therefore  number  of  the  rods  and  cones  of 
the  bacillary  layer.  Also  the  perpendicular  direction 
of  the  rods  and  cones  to  the  retinal  concave  is  probably 
related  to  the  direction  of  projection  of  impressions 
into  space,  and  therefore  to  the  accuracy  of  the  percep- 
tion of  direction. 

Illustrations  of  the  Law  of  Direction.— There  are 
many  interesting  phenomena  explained  by  this  law, 
which  thus  become  illustrations  of  the  law. 

Since  inverted  images  on  the  retina  are  reinverted 
in  projection  and  seen  erect,  it  is  evident  that  shadows 
of  objects  thrown  on  the  retina,  not  being  inverted, 
ought  to  become  inverted  in  outward  projection,  and 
therefore  seen  in  this  position  in  space.  This  is  beau- 
tifully shown  in  the  following  experiment. 

Experiment  1. — Make  a  pin-hole  in  a  card,  and, 
holding  the  card  at  four  or  five  inches  distance  against 
the  sky  before  the  right  eye  with 
the  left  eye  shut,  bring  the  pin-head 


very  near  to  the  open  eye,  so  that  it 
touches  the  lashes,  and  in  the  line  of 
sight :  a  perfect  inverted  image  of 
the  pin-head  will  be  seen  in  the  pin- 
hole.  If,  instead  of  one,  we  make 
several  pin-holes,  an  inverted  image 
of  the  pin-head  will  be  seen  in  each 
pin-hole,  as  shown  in  Fig.  26.  The  explanation  is  as 
follows  :  If  the  pin  were  farther  away,  say  six  inches  or 


FUNCTION  OF  THE   RETINA. 


87 


more,  then  light  from  the  pin  would  be  brought  to  focal 
points  and  produce  an  image  on  the  retina;  and  this 
image,  being  inverted,  would  by  projection  be  rein- 
verted,  and  the  pin  would  be  seen  in  its  real  position. 
In  the  above  experiment,  however,  the  pin  is  much  too 
near  the  retina  to  form  an  image.  But  nearness  to  the 
retinal  screen,  though  unfavorable  for  producing  an 
image,  is  most  favorable  for  casting  a  sharp  shadow ; 
and  while  retinal  images  are  inverted,  retinal  shadows 
are  erect.  The  light  streaming  through  the  pin-hole 
into  the  eye  casts  an  erect  shadow  of  the  pin-head  on 
the  retina.  This  shadow  is  projected  outward  into 
space,  and  by  the  law  of  direction  is  inverted  in  the 
act  of  projection,  and  therefore  seen  in  this  position  in 
the  pin-hole.  It  is  further  proved  to  be  the  outward 
projection  of  a  retinal  shadow 
by  the  fact  that,  by  multiplying 
the  pin-holes  or  sources  of  light, 
we  multiply  the  shadows,  pre- 
cisely as  shadows  of  an  object  in 
a  room  are  multiplied  by  multi- 
plying the  lights  in  the  room.* 

Experiment  3. — If  we  look 
at  a  strong  light,  such  as  the 
flame  of  a  candle  or  lamp,  or  a 
gas-flame,  at  some  distance  and 
at  night,  and  thus  bring  the  lids 
somewhat  near  together,  we  ob- 
serve long  rays  streaming  from 
the  light  in  many  directions,  but  chiefly  upward  and 
downward.  Fig.  27  gives  the  phenomenon  as  I  see  it. 
The  explanation  is  as  follows  :  In  bringing  the  lids  near 

*  This  phenomenon  was  first  explained  by  the  author  in  1871.     See 
"Philosophical  Magazine,"  vol.  Ixi,  p.  266. 


88 


MONOCULAR  VISION. 


together,  the  moisture  which  suffuses  the  eye  forms  a 
concave  lens,  as  in  Fig.  28  (hence  the  phenomenon  is 
much  more  conspicuous  if  there  be  considerable  moisture 
in  the  eyes).  This  watery  lens  will  be  saddle-shaped — 
i.  e.,  concave  vertically  and  convex  horizontally.  Now 
the  rays  from  the  light  (Z,  Fig.  27)  which  penetrate  the 
center  of  the  pupil  will  pass  directly  on  without  refrac- 
tion except  what  is  normal,  and  make  its  image  (Fig, 


Fio.  28. 


28,  Z')  on  the  central  spot.  But  the  rays  which  strike 
the  curved  surface  of  the  watery  lens  will  be  bent  upward 
to  ~b  and  downward  to  a.  Thus  the  light,  instead  of 
being  brought  to  a  focal  point,  is  brought  to  a  long 
focal  line,  5  $,  on  the  retina,  with  the  image  of  the  light 
in  the  middle  at  L '.  The  upper  portion  of  this  line 
~b  L'  will  be  projected  outward  and  downward,  and  form 
the  downward  streamers  of  Fig.  27;  while  the  lower 
portion  of  the  retinal  impression  a  L1  will  be  projected 
outward  and  upward,  and  form  the  upward  streamers 
of  Fig.  27.  To  prove  this,  while  the  streamers  are 
conspicuous,  with  the  finger  lift  up  the  upper  lid :  im- 
mediately the  lower  streamers  disappear;  now  press 
down  the  lower  lid :  immediately  the  upper  streamers 


FUNCTION   OF   THE   RETINA.  89 

disappear.  Also,  by  shutting  alternately  one  eye  and 
the  other,  it  will  be  seen  that  a  b  (Fig.  27)  belongs  to 
the  right  eye  and  a!  V  to  the  left. 

The  much  lighter  diverging  side-rays  are  more  dif- 
ficult to  account  for.  I  attribute  them  to  the  slight 
crinkling  of  the  mucus  covering  the  cornea  in  bringing 
the  lids  together. 


PAET  II. 
BINOCULAR    VISION. 


CHAPTER  I. 

SINGLE  AND  DOUBLE  IMAGES. 

The  Two  Eyes  a  Single  Instrument.— We  have  thus 
far  treated  only  of  the  phenomena  of  monocular  vision ; 
and  all  that  we  have  said  might  still  apply,  almost  word 
for  word,  if,  like  the  Cyclops  Polyphemus,  we  had  but 
one  eye  in  the  middle  of  the  forehead.  But  we  have 
two  eyes ;  and  these  are  not  to  be  considered  as  mere 
duplicates,  so  that  if  we  lose  one  we  still  have  another. 
On  the  contrary,  the  two  eyes  act  together  as  one  in- 
strument ;  and  there  are  many  visual  phenomena,  and 
many  judgments  based  upon  these  phenomena,  which 
result  entirely  from  the  use  of  two  eyes  as  one  instru- 
ment. These  form  the  subject  matter  of  Binocular 
Vision.  It  must  be  clearly  understood  that  the  distinc- 
tive phenomena  of  binocular  vision  require  two  eyes 
acting  as  one.  We  might  have  two  eyes,  or  even,  like 
Argus,  a  hundred  eyes,  and  yet  not  enjoy  the  advan- 
tages of  binocular  vision  ;  for  each  eye  might  see  inde- 
pendently. This  would  still  be  monocular  vision. 

The  phenomena  of  binocular  vision  are  far  less 
purely  physical  than  those  of  monocular  vision.  They 


SINGLE  AND  DOUBLE  IMAGES.  91 

are  also  far  more  obscure,  illusory,  and  difficult  of  an- 
alysis, because  far  more  subjective  and  far  more  closely 
allied  to  psychical  phenomena.  From  early  childhood 
I  have  amused  myself  with  experiments  in  this  field, 
and  have  thus  acquired  an  unusual  voluntary  power 
over  the  movements  of  the  eyes,  and  a  still  more  un- 
usual power  of  analysis  of  visual  phenomena.  This  has 
always  therefore  been  a  favorite  field  for  me ;  but  with 
a  little  practice  any  one  may  acquire  similar  power  and 
enjoy  a  similar  pleasure. 

Binocular  Field. — We  have  said  that  the  field  of 
view  is  naught  else  than  an  outward  projection  of  ret- 
inal states.  With  the  eyes  open  and  the  retina  in  an 
active  or  stimulated  condition,  we  call  it  the  field  of 
view ;  with  the  eyes  shut  and  the  retina  in  a  compara- 
tively passive  or  unstimulated  condition,  we  call  it  the 
field  of  darkness.  In  either  case,  every  variation  in 
the  state  of  different  parts  of  the  retina,  whether  by 


shadows  or  by  images,  or  by  its  own  internal  changes 
or  unstimulated  activity,  is  faithfully  represented  in 
external  space  by  spectra,  external  images,  etc.  But 
we  have  two  eyes,  and  therefore  two  retinae,  and  there- 
fore also  two  fields  of  view,  the  external  projections  of 


92  BINOCULAR  VISION. 

the  two  retinae.  These  two  fields  of  view  partly  over- 
lap each  other,  so  as  to  form  a  common  or  binocular 
field.  Fig.  29  represents  roughly  the  form  of  these 
fields  in  my  own  case.  The  right  field,  R,  is  bounded 
by  the  line  of  the  nose  n  n  on  the  left,  the  brows  br 
above,  and  the  cheek  ch  below.  The  field  of  the  left 
eye,  L,  is  bounded  similarly  on  the  right  by  the  nose 
n'  n',  the  brow  ~br ',  and  the  cheek  ch' .  Between  the 
lines  of  the  nose,  n  n,  n!  nf,  is  the  rounded  triangu- 
lar space  C  F)  which  is  the  common  or  binocular  field. 
This  common  field  is  the  only  part  seen  by  both  eyes. 
The  two  fields  are  left  vacant  on  the  extreme  right  and 
left,  because,  projected  on  a  plane  surface,  they  are  un- 
limited in  these  directions.  This  is  the  necessary  result 
of  the  fact  that  in  a  horizontal  direction  the  field  of  view 
of  both  eyes  is  more  than  180°. 

Now,  there  being  two  retinae,  there  are  of  course 
two  retinal  images  of  every  external  object ;  and  since 
retinal  images  are  projected  outward  into  space  as  ex* 
ternal  images,  we  must  have  two  external  images  of 
every  object.  But  we  see  objects  only  by  these  exter- 
nal images.  Why,  then,  with  twTo  retinal  images — ay, 
and  two  external  images — for  every  object,  do  we  not 
see  all  objects  double  f  I  answer :  We  do  indeed  see 
all  objects  double,  except  under  certain  conditions. 

Double  Images. — This  phenomenon  of  double  images 
of  all  objects,  except  under  certain  special  conditions,  is 
so  fundamental  in  binocular  vision,  and  yet  so  commonly 
overlooked  by  even  the  most  intelligent  persons  unac- 
customed to  analyze  their  visual  impressions,  that  it 
becomes  absolutely  necessary  first  of  all  to  prove  it  by 
detailing  many  experiments,  which  every  one  may  re- 
peat for  himself. 

Experiment  1. — Holding  up  the  finger  before  the 


SINGLE  AXD  DOUBLE  IMAGES.  93 

eyes,  look,  not  at  the  finger,  but  at  the  wall  or  the  ceil- 
ing or  the  sky.  Two  transparent  images  of  the  finger 
will  be  seen,  the  left  one  belonging  to  the  right  eye 
and  the  right  one  to  the  left  eye.  We  easily  prove  this 
by  shutting  first  one  and  then  the  other  eye,  and  observ- 
ing which  image  disappears.  The  images  are  trans- 
parent, or  shadowy,  because  they  do  not  conceal  any- 
thing. The  place  covered  by  the  right-eye  image  is 
seen  by  the  left  eye,  and  the  place  covered  by  the  left- 
eye  image  is  seen  by  the  right  eye.  If  we  alternately 
shut  one  eye  and  then  the  other,  the  wide  difference 
between  these  places  is  at  once  evident.  Often  there 
is  an  alternation  in  the  distinctness  of  these  shadowy 
images — first  one  and  then  the  other  fading  away,  and 
almost  disappearing  from  view. 

Experiment  2. — Point  with  the  forefinger  at  some 
distant  object,  looking  with  both  eyes  open  at  the  ob- 
ject, not  the  finger.  Two  fingers  will  be  seen,  one  of 
them  pointing  at  the  object  and  the  other  far  out  of 
range,  usually  to  the  right. 

Most  persons  find  some  difficulty  at  first  in  being 
conscious  of  perceiving  two  images.  The  reason  is, 
they  do  not  easily  separate  what  they  know  from  what 
they  see.  They  know  there  is  but  one  finger,  and 
therefore  they  think  they  see  but  one.  The  best  plan 
is  to  shut  alternately  one  eye  and  then  the  other,  and 
observe  the  places  of  projection  of  the  finger  against 
the  wall ;  and  then,  opening  both  eyes,  shadowy  im- 
ages at  both  these  places  will  be  seen.  I  have  found 
some  trouble  in  convincing  a  few  persons,  and  have 
found  one  single  person  whom  I  could  not  convince, 
that  there  were  two  images.  To  such  a  person  all  that 
I  am  about  to  say  on  binocular  vision  will  be  utterly 
unintelligible.  The  whole  cause  of  the  difficulty  in 


94:  BINOCULAR  VISION. 

perceiving  at  once  double  images  is,  that  we  habitually 
neglect  one  image  unless  attention  is  specially  drawn 
to  it.  I  have  found  that  nearly  all  persons  neglect 
the  right-hand  image — i.  e.,  the  image  belonging  to 
the  left  eye.  In  other  words,  they  are  Tight-eyed  as 
well  as  right-handed.  I  have  also  tried  the  same  ex- 
periment on  several  left-handed  persons,  and  have  found 
that  these  neglected  the  left  image — i.  e.,  the  image  be- 
longing to  the  right  eye.  In  other  words,  they  were 
left-eyed  as  well  as  left-handed.  There  is  no  doubt 
that  dextrality  affects  the  whole  side  of  the  body,  and 
is  the  result  of  greater  activity  of  the  left  cerebral 
hemisphere.  People  are  right-handed  because  they  are 
left-drained. 

I  pause  a  moment  in  order  to  draw  attention  here 
to  the  uncertainty  of  some  so-called  facts  of  conscious- 
ness. I  have  often  labored  to  convince  a  person,  un- 
accustomed to  analyze  his  visual  impressions,  of  the 
existence  of  double  images  in  his  own  case.  He  would 
appeal  with  confidence,  perhaps  with  some  heat,  to  his 
consciousness  against  my  reason ;  and  yet  he  would 
finally  admit  that  I  was  right  and  he  was  wrong.  So- 
called  facts  of  consciousness  must  be  scrutinized  and 
analyzed,  and  subjected  to  the  crucible  of  reason,  as 
well  as  other  supposed  facts,  before  they  should  be  re- 
ceived. 

Experiment  3. — Place  the  two  forefingers,  one  be- 
fore the  other,  in  the  middle  plane  of  the  head  (i.  e., 
the  vertical  plane  through  the  nose,  and  dividing  the 
head  into  two  symmetrical  halves),  and  separated  by  a 
considerable  distance — say  one  8  inches  and  the  other 
18  to  20  inches  from  the  eyes.  Now,  if  we  look  at 
the  farther  finger,  it  will  be  of  course  seen  single,  but 
the  nearer  one  is  double ;  if  we  look  at  the  nearer 


SIXGLE  AND  DOUBLE  IMAGES. 


95 


finger,  this  will  be  seen  single,  but  the  farther  one  is 
now  double ;  but  it  is  impossible  to  see  both  of  them 
as  single  objects  at  the  same  time.  By  alternately 
shutting  one  eye  and  then  the  other,  we  can  observe 
in  either  case  which  of  the  double  images  disappears. 
Thus  we  will  learn  that  when  we  look  at  the  farther 
finger,  the  nearer  one  is  so  doubled  that  the  left  image 
belongs  to  the  right  eye  and  the  right  image  to  the  left 
eye  ;  while,  on  the  contrary,  when  we  look  at  the  nearer 
finger,  the  farther  one  is  so  doubled  that  the  right  image 
belongs  to  the  right  eye  and  the  left  image  to  the  left 
eye.  In  the  former  case  the  images  are  said  to  be  het- 
eronymous,  i.  e.,  of  different  name,  and  in  the  latter 
case  they  are  said  to  be  homonymous,  i.  e.,  of  the  same 
name,  as  the  eye. 

Analogues  of  Double  Images  in  Other  Senses.— When- 
ever it  was  possible,  we  have  traced  the  analogy  of 
visual  phenomena  in  other  senses.  Is 
there  any  analogue  of  double  vision  to 
be  found  in  other  senses?  There  is, 
as  may  be  shown  by  the  following  ex- 
periment :  If  we  cross  the  middle  fin- 
ger over  the  forefinger  until  the  points 
are  well  separated,  and  then  roll  a  small 
round  body  like  a  child's  marble  about 
on  the  table  between  the  points  of  the 
crossed  fingers,  we  will  distinctly  per- 
ceive two  marbles.  The  points  of  the 
fingers  touched  by  the  marble  are  non- 
corresponding.  (Fig.  30.) 

Single  Vision. — Therefore  it  is  evident  that  when 

we  look  directly  at  anything  we  see  it  single,  but  that 

all  things  nearer  or  beyond  the  point  of  sight  are  seen 

double.     We  then  come  back  to  our  previous  proposi- 

5 


FIG.  80. 


96 


BINOCULAR  VISION. 


tion,  that  we  always  see  tilings  double  except  under 
certain  conditions.  What,  then,  are  the  conditions  of 
single  vision  ?  I  answer  :  We  see  a  thing  single  when 
the  two  images  of  that  thing  are  projected  outward  to 
the  same  spot  in  space,  and  are  therefore  superposed 
and  coincide.  Under  all  other  conditions  we  see  them 
double.  Again,  the  two  external  images  of  an  object 
are  thrown  to  the  same  spot,  and  thus  superposed  and 
seen  single,  when  the  two  retinal  images  of  that  object 
fall  on  wThat  are  called  corresponding  points  (or  some- 
times identical  points)  of  the  two  retinae.  If  they  do 
not  fall  on  corresponding  points  of  the  two  retinae,  then 
the  external  images  are  thrown  to  different  places  in 
space,  and  therefore  seen  double.  We  must  now  explain 
the  position  of  corresponding  points  of  the  two  retinae. 
Corresponding  Points.— The  retinae,  as  already  seen, 
are  two  deeply  concave  or  cup-shaped  expansions  of  the 
optic  nerve.  If  R  and  Z,  Fig.  31,  represent  a  projec- 
tion of  these  two  retinal  cups,  then  the  black  spots  C  C'* 


Fo.  81. 


in  the  centers  of  the  bottom,  will  represent  the  position 
of  the  central  spots.  If  now  we  draw  vertical  lines 
(vertical  meridians),  a  J,  a'  £',  through  the  central  spots, 
so  as  to  divide  the  retinae  into  two  equal  halves,  then 
the  right  halves  would  correspond  point  for  point,  and 


SINGLE   AND   DOUBLE  IMAGES.  97 

the  left  halves  would  correspond  point  for  point ;  i.  e., 
the  internal  or  nasal  half  of  one  retina  corresponds  with 
the  external  or  temporal  half  of  the  other,  and  vice 
versa.  Or,  more  accurately,  if  the  concave  retinae  be 
covered  with  a  system  of  rectangular  spherical  coordi- 
nates, like  the  lines  of  latitude  and  longitude  of  a  globe, 
a  5  and  x  y  being  the  meridian  and  equator,  then  points 
of  similar  longitude  and  latitude  in  the  two  retinae,  as 
d  d' ,  e  e',  are  corresponding.  Or,  still  better,  suppose 
the  two  eyes  or  the  two  retinae  to  be  placed  one  upon 
the  other,  so  that  they  coincide  throughout  like  geomet- 
ric solids ;  then  the  coincident  points  are  also  corre- 
sponding points.  Of  course,  the  central  spots  will  be 
corresponding  points  ;  also  points  on  the  vertical  merid- 
ians, a  J,  aJ  5',  at  equal  distances  from  the  central  spots, 
will  be  corresponding ;  also  points  similarly  situated  in 
similar  quadrants,  as  d  d ,  e  e' ,  etc.  It  is  probable  that 
the  definition  just  given  is  not  mathematically  exact  for 
some  eyes.  It  is  probable  that  in  some  eyes  the  appar- 
ent vertical  meridian  which  divides  the  retinae  into  cor- 
responding halves  is  not  perfectly  vertical,  but  slightly 
inclined  outward  at  the  top.  This  would  affect  all  the 
meridians  slightly ;  but  the  effect  is  very  small,  and  I 
do  not  find  it  so  in  my  eyes.  We  shall  discuss  this 
point  again  (page  146). 

Law  of  Corresponding  Points. — After  this  explanation 
we  reenunciate  the  law  of  corresponding  points :  Objects 
are  seen  single  when  their  retinal  images  fall  on  corre- 
sponding points.  If  they  do  not  fall  on  corresponding 
points,  their  external  images  are  thrown  to  different 
places  in  space,  and  therefore  are  seen  double. 

Thus  we  see  that  the  term  "  corresponding  points  " 
is  used  in  two  senses,  which  must  be  kept  distinct  in 
the  mind  of  the  reader.  Every  rod  and  cone  in  each 


98 


BINOCULAR  VISIOX. 


retina  has  its  correspondent  in  external  space,  and  these 
exchange  with  each  other  by  impression  and  projection. 
Also  every  rod  or  cone  of  each  retina  has  its  correspon- 
dent in  a  rod  or  cone  in  the  other  retina.  Now  the  law 
of  corresponding  points,  with  which  we  are  now  deal- 
ing, states  that  the  two  external  or  spatial  correspon- 
dents of  two  retinal  corresponding  points  always  coin- 

FIG.  32. 
A 


R  and  Z,  two  eyes ;  0,  center  of  rotation  of  ball,  or  optic  center ;  ce,  point  of  crossing1 
of  ray-lines — nodal  point ;  A,  point  of  sight;  Z>,  some  other  point  in  the  horoptoric 
circle  A  O  0' ;  c  c',  central  spots ;  aa',d  d\  actual  images  of  A  and  D. 

cide  with  each  other.  In  order  to  distinguish  these  two 
kinds  of  corresponding  points  from  each  other,  the  lat- 
ter— i.  e.,  corresponding  points  on  the  two  retinae — are 
often,  and  perhaps  best,  called  "identical  points,"  be- 
cause their  external  spatial  representatives  are  really 
identical. 

"We  will  now  apply  the  law.     If  we  look  directly  at 


SINGLE   AND   DOUBLE   IMAGES.  99 

any  small  object,  it  will  be  seen  single,  because  the  two 
retinal  images  fall  on  corresponding  or  identical  points, 
viz.,  on  the  two  central  spots.  In  Fig.  32  the  two  eyes, 
It  and  Z,  are  turned  directly  on  A.  The  image  of  this 
object  will  therefore  fall  on  the  central  spots  c  c',  and 
the  object  will  be  seen  single.  Objects  at  nearly  the 
same  distance,  as  for  example  D,  a  little  to  the  right  or 
left  or  a  little  above  or  below  the  point  of  sight,  are  also 
seen  single ;  because  the  retinal  images  d  and  d '  are  on 
correspondent  halves — i.  e.,  the  internal  or  nasal  half  of 
R  and  the  external  or  temporal  half  of  L — and  at  the 
same  distance  from  the  central  spots  c  c',  and  therefore 
on  identical  points.  Objects  lying  in  a  horizontal  cir- 
cle passing  through  the  point  of  sight  and  the  centers 
of  the  eyes,  0  0 ',  are  usually  supposed  to  be  seen  single. 
This  is  nearly  true,  except  when  the  point  of  sight  is 
very  near.  This  circle  has  been  called  the  horopterio 
circle  of  Miiller. 

Objects,  as  already  said,  beyond  or  nearer  than  the 
point  of  sight,  are  always  seen  double.  The  reason  is, 
that  their  retinal  images  always  fall  on  non-correspond- 
ing points.  This  is  shown  in  the  diagram  Fig.  33. 
While  the  two  eyes,  It  and  Z,  are  fixed  upon  A,  this 
object  will  be  seen  single,  for  its  images,  a  and  a!,  fall 
upon  the  central  spots.  But  if,  while  still  looking  at 
A,  we  observe  B  and  C,  we  shall  see  that  both  are 
double.  The  reason  is,  that  the  images  of  B,  viz.,  J  5', 
fall  upon  the  two  nasal  or  internal  halves  of  the  retinae, 
which  are  non-corresponding;  while  the  images  of  C, 
viz.,  c  c',  fall  upon  the  two  external  or  temporal  halves 
of  the  retinse,  which  are  also  non-corresponding.  If 
the  external  double  images  be  all  referred  to  the  plane  of 
sight,  P  P  (which,  however,  is  not  the  fact),  as  is  usually 
represented'  in  diagrams,  then  the  portion  of  the  dou- 


100 


BINOCULAR    VISION. 


ble  images  will  be  correctly  represented  by  c  c',  bbf. 
It  is  seen  at  a  glance  that  the  images  c  c'  of  C  are  het- 
eronymous,  while  the  images  &  $'  of  B  are  homony- 
mous.  Generally,  all  the  field  of  view  within  the  lines 


of  sight,  A  a,  A  a' ,  belongs  to  the  temporal  halves  of 
the  retinae,  while  all  outside  of  these  lines  belongs  to 
the  nasal  halves.  Or,  again,  double  images  formed  by 
impressions  on  the  two  nasal  halves  of  the  retinae  are 
while  those  formed  by  impressions  on 
.halves  are  heteroriymous.  '  •  • 


SINGLE  AND  DOUBLE   IMAGES.  1Q1 

Definition  of  Horopter. — We  have  seen  that  the  ob- 
ject at  the  point  of  sight  is  seen  single ;  and  all  objects 
at  the  same  or  nearly  the  same  distance,  but  a  little  to 
the  right  or  left,  or  above  or  below,  are  also  either 
seen  single,  or  else  the  doubling,  if  any,  is  usually  im- 
perceptible. On  the  contrary,  all  objects  farther  or 
nearer  than  the  point  of  sight  are  seen  double.  Now 
the  surface  of  single  vision — i.  e.,  the  surface  passing 
through  the  point  of  sight,  all  the  objects  lying  in 
which  are  seen  single — is  called  the  horopter.  Whether 
there  is  such  a  surface  at  all,  and  if  there  is,  what  is  its' 
form,  are  questions  upon  which  the  acutest  observers 
differ.  Some  have  made  it  a  plane,  some  a  spherical 
surface.  Some,  by  purely  geometrical  methods,  have 
given  it  the  most  curious  forms  and  properties ;  while 
others,  by  purely  experimental  methods,  have  come  to 
the  conclusion  that  it  is  not  a  surface  at  all,  but  a  line. 
We  are  not  now  prepared  to  discuss  this  question,  but 
shall  return  and  devote  to  it  a  special  chapter. 

Supposed  Relation  of  the  Optic  Chiasm  to  the  Law  of 
Corresponding  Points, — In  the  optic  chiasm,  Fig.  20, 
page  54,  there  is  certainly  a  partial  (but  only  a  partial) 
crossing  of  the  fibers  of  the  two  optic  nerves.  Many 
physiologists  connect  this  fact  with  this  remarkable  law. 
There  is  probably  such  a  connection.  But  many  go  far- 
ther. They  think  that  some  of  the  fibers  of  each  optic 
nerve  cross  over  to  the  other  eye,  and  some  do  not ;  and 
that  those  which  cross  over  supply  the  internal  or  nasal 
halves,  and  those  which  do  not  cross  over  supply  the 
temporal  halves.  Thus,  in  the  diagram  Fig.  34:,  the 
fibers  of  the  right  optic  nerve-root  0,  as  it  comes  from 
the  brain,  go  to  supply  the  temporal  half  t  of  the  right 
retina,  and,  by  crossing,  the  nasal  half  n'  of  the  left  ret- 
ina, and  these  are  corresponding  halves.  So  also  the 


102  BINOCULAR  VISION. 

fibers  of  the  left  optic  nerve-root  O'  go  to  supply  the 
temporal  half  t'  of  the  left  and  nasal  half  n  of  the  right 
retina.  Still  further,  they  think  that  the  fibers  coming 
from  corresponding  or  identical  points,  or  rods,  or  cones 

FIG.  34. 


0' 

0  0',  optic  roots;  N  N',  optic  nerves ;  R  and  L,  sections  of  the  two  eyes ;  c  c',  cen- 
tral spots;  n  n',  ths  nasal  halves,  and  1 1',  the  temporal  halves,  of  the  retinae. 

in  the  two  retinae  are  not  only  thus  carried  by  the  same 
optic  root,  but  finally  unite  to  form  one  fiber,  or  at  least 
terminate  centrally  in  one  brain-cell,  and  thus  form  one 
single  sense-impression.  It  is  almost  needless  to  say 
that,  while  this  is  an  interesting  speculation,  it  is  no- 
thing more ;  for  the  supposed  union  of  fibers  from  cor- 
responding rods  or  cones  can  probably  never  be  either 
proved  or  disproved. 

Theories  of  the  Origin  of  this  Law.— The  perception 
of  direction  and  the  correspondence  of  retinal  and  spa- 
tial points  are  certainly  inherent  properties  of  the  ret- 
ina, being  connected  with  its  structure.  The  former — 
i.  e.,  the  perception  of  direction — we  have  seen,  is  a 
general  property  of  sensory  nerves,  only  developed  into 
mathematical  accuracy  in  the  case  of  the  optic  nerve ; 


SINGLE  AND   DOUBLE  IMAGES.  1Q3 

the  latter — i.  e.,  the  correspondence  of  retinal  and  spa- 
tial points — is  only  the  expression  of  this  mathematical 
accuracy  of  perception  of  direction ;  and  both  are  con- 
nected with  the  structure  of  the  bacillary  layer.  Un- 
doubtedly, then,  this  property  is  innate  and  antecedent 
to  all  experience.  What  the  infant  learns  by  experience 
is  not  direction,  but  distance  and  size  of  the  object. 
Direction  is  a  primary  datum  of  sense.  But  the  prop- 
erty of  corresponding  points  of  the  two  retinae  and  of  W .  \ 
identical  spatial  points  in  the  two  fields  of  view  seems  to 
be  less  absolutely  simple  and  primary.  The  questions, 
"  Is  this  property  innate,  instinctive,  antecedent  to  ex- 
perience? or  is  it  wholly  the  result  of  experience?" 
have  been  long  and  hotly  disputed  by  the  profoundest 
thinkers  on  this  subject.  The  former  view  has  been 
held  by  Miiller,  Pictet,  and  others ;  the  latter  by  Helm-  , 
holtz,  Briicke,  Prevost,  and  Giraud  Teulon :  the  one  is 
called  the  nativistic,  the  other  the  empiristic  theory. 

We  shall  not  follow  the  history  of  this  dispute,  nor 
detail  the  arguments  brought  forward  on  each  side ;  for 
the  tendency  of  modern  science,  under  the  guidance  of 
the  theory  of  evolution,  is  to  bring  these  two  opposite 
views  together,  and  reconcile  them  by  showing  that 
they  are  both  in  a  degree  true,  and  therefore  not  wholly 
inconsistent  with  each  other.  The  difficulty  heretofore 
has  been  that  anatomists  and  physiologists  have  studied 
man  too  much  apart  from  other  animals,  and  thus  the 
amount  of  inherited,  innate,  instinctive  qualities  has 
been  greatly  underestimated  by  some  and  overestimated 
by  others.  A  new-born  chicken,  in  a  few  minutes  after 
breaking  the  egg-shell,  will  see  an  object,  direct  the 
eyes  upon  it,  walk  straight  up  to  it,  and  seize  it.  Evi- 
dently there  is  in  this  case  not  only  a  perception  of 
direction,  antecedent  to  all  experience,  but  also  some 


104:  BINOCULAR  VISION. 

perception  of  distance,  and  the  wonderful  coordination 
of  muscles  necessary  for  standing  and  walking,  and 
directing  the  movements  of  the  eyes.  A  young  rumi- 
nant animal  in  a  few  minutes  after  birth  will  stand  and 
walk,  and  direct  its  motions  by  sight.  A  bird  of  wild 
species,  hatched  in  a  cage  and  kept  in  a  cage  until  it  is 
fully  fledged  and  its  muscles  are  sufficiently  developed, 
if  then  thrown  into  the  air,  will  fly  *away  with  ease, 
although  the  coordination  of  many  muscles  in  the  act 
of  flying  is  something  so  marvelous  that  it  could  not  be 
learned  in  a  lifetime  of  trial,  unaided  by  inherited  ca- 
pacity. Inherited  powers  are  still  more  marvelous  in 
the  case  of  insects. 

Manifestly,  then,  the  wealth  of  capacities  in  all  di- 
rections possessed  by  the  individual  is  partly  inherited 
and  partly  acquired  by  individual  experience.  In  ani- 
mals the  inherited,  in  man  the  individually  acquired, 
wealth  predominates.  But  all  wealth  is  acquired.  Even 
that  inherited  is  ancestral  experience  accumulated  and 
transmitted  by  the  law  of  heredity.  Even  instinct  is 
"  inherited  experience."  Thus,  then,  it  is  evident  that 
the  property  of  corresponding  points  of  the  two  retinae, 
and  therefore  of  identical  points  in  space,  is  partly  in- 
herited and  partly  acquired  by  individual  experience. 
It  is  doubtless  wholly  the  result  of  experience,  but  not 
wholly  of  individual  experience. 

Consensual  Adjustments.— There  are  therefore  two 
adjustments  of  the  eye  in  every  voluntary  act  of  sight, 
viz.,  focal  and  axial.  In  the  former,  each  eye  is  adjusted 
by  the  ciliary  muscle  to  make  a  perfect  image  on  the 
retina ;  in  the  latter,  the  two  eyes  are  turned  by  the 
recti  muscles  so  that  their  axes  shall  meet  on  the  point 
of  sight,  and  the  images  of  the  object  looked  at  shall 
fall  on  the  central  spots.  The  one  is  an  adjustment  for 


SINGLE  AND   DOUBLE  IMAGES.  105 

distinct  vision,  the  other  for  single  vision.  There  is 
associated  with  these  still  a  third  adjustment,  but  of 
far  less  importance,  viz.,  the  adjustment  of  the  pupil. 
The  pupil  contracts  and  expands  not  only  as  the  light 
is  bright  or  faint,  but  also  as  the  object  is  near  or  far. 
These  three  adjustments  take  place  together  and  with- 
out distinct  volition  for  each — i.  e.,  by  the  one  volun- 
tary act  of  looking.  They  are  therefore  consensual 
movements,  and  usually  regarded  as  indissolubly  asso- 
ciated. We  shall  show  hereafter  that  under  certain 
circumstances  they  may  be  dissociated. 

The  two  Fundamental  Laws.— There  are  also  two 
great  and  fundamental  laws  by  which  all  visual  phe- 
nomena are  explained,  viz.,  the  law  of  direction  and 
the  law  of  corresponding  points.  The  one  gives  the 
true  position  of  all  points  in  space,  and  therefore  en- 
tirely explains  the  apparent  anomaly  of  erect  vision 
with  inverted  retinal  images ;  the  other  gives  coinci- 
dence of  corresponding  points  in  the  two  fields  of  view, 
and  therefore  entirely  explains  the  second  anomaly  of 
single  vision  with  two  retinal  images.  Both  may  in 
fact  be  called  laws  of  corresponding  points.  The  one 
asserts  the  correspondence  point  for  point  of  retinal 
rods  and  cones  with  external  space,  with  ray-lines  con- 
necting and  crossing  in  the  nodal  point ;  the  other 
asserts  a  correspondence  point  for  point  of  the  rods 
and  cones  of  the  two  retinae,  and  the  coincidence  of 
their  representatives  in  the  two  fields  of  view.  From 
the  one  law  flow  all  the  phenomena  of  monocular,  from 
the  other  all  the  phenomena  of  'binocular  vision. 

All  the  phenomena  of  binocular  vision  are  explained 
by  the  law  of  corresponding  points.  But  the  phenom- 
ena are  so  numerous,  so  illusory,  and  so  difficult  of 
analysis,  that  the  connection  is  by  no  means  obvious. 


106  BINOCULAR  VISION. 

The  science  of  binocular  vision  consists  in  tracing  this 
connection,  and  thus  explaining  the  phenomena.  It 
will  be  our  object,  then,  to  take  up  all  the  most  impor- 
tant phenomena  of  binocular  vision,  and  explain  them 
in  this  way. 


CHAPTER  II. 

SUPERPOSITION  OF  EXTERNAL  IMAGES. 

IN  the  movements  of  one  eye,  or  of  the  two  eyes  if 
they  move  together  equally  in  the  same  direction,  as  in 
looking  to  one  side  or  the  other,  or  up  or  down,  ob- 
jects seem  to  stand  still,  and  the  eyes  or  the  point  of 
sight  to  sweep  over  them.  But  if  we  move  the  eyes  in 
opposite  directions,  as  in  converging  the  optic  axes 
strongly  and  then  allowing  them  to  become  again  par- 
allel, objects,  or  rather  their  external  images,  seem  to 
sweep  like  trooping  shadows  across  the  field  of  view ; 
or  rather,  the  fields  of  view  themselves  seem  to  rotate, 
carrying  all  their  images  with  them,  in  a  direction  con- 
trary to  the  motion  of  the  eye,  and  therefore  (since  the 
two  eyes  move  in  contrary  directions)  in  directions  con- 
trary to  each  other.  This  phenomenon  is  not  very  easily 
observed,  because  it  is  best  seen  by  simple  convergence 
of  the  eyes  on  a  very  near  point  in  space,  without  any 
object  to  direct  the  convergence,  or  in  trying  to  look  at 
the  root  of  the  nose.  Divergence  of  the  eyes  may  be 
produced  by  pressing  the  fingers  in  their  external  cor- 
ners. In  this  case  also  the  motion  of  the  images  is 
evident. 

Evidently,  then,  by  voluntary  motion  of  the  eyeballs 
in  opposite  directions,  and  the  consequent  motion  of  the 


108  BINOCULAR   VISION. 

shadowy  images  in  opposite  directions,  we  may  (if  we 
observe  the  images  and  control  the  motion  of  the  eyes) 
cause  them,  whether  they  belong  to  the  same  object  or 
to  different  objects,  to  approach  each  other  and  combine 
successively.  Many  curious  phenomena  thus  result, 
which  it  is  necessary  to  understand  before  we  approach 
the  more  complex  phenomena,  and  especially  before 
we  can  explain  the  judgments  based  upon  these  phe- 
nomena. 

Combination  of  the  Images  of  Different  Objects.— We 
have  seen  that  the  combination  of  the  two  external 
images  of  the  same  object  produces  single  vision.  But 
the  external  images  of  different  objects  may  also  be 
combined.  Under  this  head  there  are  several  cases. 

1.  Dissimilar  Objects.— We  have  seen  that  when  the 
two  images  of  an  object  fall  on  corresponding  points  of 
the  two  retinae,  they  are  thrown  outward  as  external 
images  to  the  same  point  in  space,  superposed,  and 
united,  and  therefore  the  object  is  seen  single.  If,  in- 
stead of  the  two  images  of  the  same  object,  the  images 
of  twro  different  objects  fall  upon  corresponding  points, 
evidently  they  also  will  be  thrown  to  the  same  place 
in  space  and  superposed.  In  this  case,  however,  there 
being  two  objects,  there  will  be  four  retinal  images, 
only  two  of  which  will  fall  on  corresponding  points,  and 
also  four  external  images,  only  two  of  which  will  be 
superposed.  But  we  may  confine  our  attention  to  the 
superposed  images,  or  else  we  may  cut  off  the  others 
from  view,  or  prevent  them  from  forming. 

Experiment  1. — If  the  left  hand  and  the  right  fore- 
finger, or  any  two  dissimilar  objects,  be  held  up  before 
the  eyes,  say  8  to  10  inches  apart,  and  then  the  eyes  be 
converged  until  the  right  eye  looks  exactly  toward  the 
left  hand  and  the  left  eye  toward  the  right  forefinger, 


SUPERPOSITION  OF  EXTERNAL  IMAGES.  109 

then  evidently  the  retinal  images  of  these  two  objects 
will  fall  on  corresponding  points,  viz.,  on  the  central 
spots ;  and  their  corresponding  external  images  ought 
to  be  thrown  to  the  same  place  and  superposed.  Such 
is  actually  the  fact.  The  phenomena  as  they  actually 
appear  are  as  follows :  As  the  eyes  begin  to  converge, 
the  images  of  both  objects  double  homonymously,  and 
we  see  now  four  images.  As  the  convergence  increases, 
the  double  images  separate  more  and  more,  until  the 
left  image  (belonging  to  the  left  eye)  of  the  forefinger 
and  the  right  image  of  the  hand  (this  belongs  to  the 
right  eye)  are  brought  together  and  superposed,  and 
the  forefinger  is  seen  lying  in  the  palm  of  the  hand. 
Of  course,  as  already  explained,  there  will  be  two  other 
images — one  of  the  forefinger  to  the  right,  and  belong- 
ing to  the  right  eye,  and  one  of  the  hand  to  the  left, 
and  belonging  to  the  left  eye.  By  shutting  alternately 
one  eye  and  then  the  other,  these  belongings  of  the 
several  images  may  be  tested. 

Experiment  2. — Or,  again,  the  same  combination 
may  take  place  without  convergence  of  the  eyes,  thus : 
Hold  up  the  two  forefingers  before  the  eyes  a  foot  or 
so  distant,  and  a  little  more  than  two  inches  apart  (it 
should  be  equal  to  the  interocular  distance),  and  against 
a  bright  background  like  a  white  wall  or  the  sky.  Xow 
look  at  the  wall  or  the  sky :  the  two  fingers  will  both 
double,  making  four  images ;  but  the  two  middle  im- 
ages will  unite  to  form  what  seems  to  be  one  finger. 

O  -  O 

There  will  be  therefore  -apparently  three  images :  the 
middle  one  (the  combined  images)  is  opaque  like  an 
object;  the  other  two,  uncombined,  are  transparent 
like  ordinary  double  images.  In  this  case,  as  we  are 
gazing  beyond  the  finger,  the  double  images  are  het- 
eronymous.  It  is  therefore  the  right-eye  image  of  the 


110 


BINOCULAR   VISION. 


right  finger  (the  left  of  its  double  images)  and  the  left- 
eye  image  of  the  left  finger  (the  right  of  its  double 
images)  which  combine  in  the  middle. 

These  facts  and  the  conditions  under  which  the 
combination  takes  place  are  illustrated  by  the  accom- 
panying diagrams.  In  Fig.  35  the  right  eye,  It,  is 
directed  toward  the  object  B,  and  the  left  eye,  Z,  to- 


FIG.  35 


In  both  figures  the  letters  are  the  same.  R  and  Z,  the  two  eyes ;  A  and  B,  two  ob- 
jects ;  «'&,  Fig.  35,  and  aft',  Fig.  36,  combined  images  ;  primed  letters,  left-eye  im- 
ages ;  c  c,  central  spots  of  retinae ;  n,  the  nose  ;  P  P,  plane  of  objects ;  and  p  p, 
plane  of  sight. 

ward  the  object  A.  The  retinal  images  of  these,  falling 
on  the  central  spots  c  c,  are  superposed  at  the  point  of 
sight  (where  the  lines  of  sight  intersect)  and  seen  as  a'b, 
while  two  shadowy  images,  a  and  &',  are  seen  to  the  right 
and  left.  Their  position  in  the  plane  of  sight,  and  as 


SUPERPOSITION  OF  EXTERNAL  IMAGES.  HI 

determined  by  the  law  of  direction,  is  given  by  con- 
necting the  points  R  A  and  L  B.  In  Fig.  36  the  right 
eye,  R,  is  directed  toward  the  object  A,  and  the  left 
eye,  Z,  toward  the  object  B.  The  point  of  sight  is 
therefore  beyond,  at  the  meeting  of  the  optic  axes  or 
lines  of  sight.  There  the  combined  images,  aV,  will 
be  seen,  while  two  other  uncombined  images  will  be 
seen  at  points  determined  by  the  law  of  direction,  rep- 
resented by  continuing  the  lines  R  B  and  L  A  to  the 
plane  of  sight.  It  is  evident  that  in  this  case  the  two 
objects  A  and  B  must  not  be  farther  apart  than  the 
optic  centers  (interocular  space) ;  otherwise  the  lines  of 
sight  will  not  meet  in  a  point  of  sight,  and  therefore 
the  two  images  will  not  combine.  Simple  inspection 
of  the  diagrams  will  explain  the  phenomena,  if  the 
reader  will  bear  in  mind  that  capitals  represent  ob- 
jects and  small  letters  external  images ;  and  further, 
that  the  primed  small  letters  represent  left-eye  images, 
the  strong  lines  P  P  the  actual  plane  of  the  objects, 
and  the  dotted  lines  p  p  the  plane  of  sight  or  of  the 
images. 

Many  persons  will  not  at  first  succeed  in  making 
these  experiments,  on  account  of  the  difficulty  which 
most  persons  experience  in  watching  double  images  and 
controlling  the  movements  of  the  eyes.  To  such  we 
would  recommend  the  following  method :  Let  the  two 
objects  set  up  before  the  eyes  in  the  first  experiment  be 
other  than  parts  of  the  body  of  the  observer — for  ex- 
ample, a  card  and  a  rod,  or  two  rods.  Then,  while 
looking  at  the  table  on  which  the  objects  lie,  hold  up 
the  forefinger — or  better,  a  pencil — -between  the  eyes 
and  the  objects.  The  pencil  will  of  course  be  double. 
Now,  by  bringing  the  pencil  nearer  or  carrying  it  far- 
ther, its  double  images  will  separate  or  close  up.  Bring 


112  BINOCULAR   VISION. 

the  pencil  into  such  a  position  that  its  double  images 
shall  exactly  coincide  with  the  centers  of  the  two  ob- 
jects which  you  desire  to  combine.  If  you  now  look 
at  the  pencil,  the  ocular  convergence  will  be  exactly 
suitable  for  combining  the  objects. 

In  the  cases  thus  far  mentioned  there  is  no  illusion : 
the  combined  images  do  not  produce  the  appearance  of 
a  real  object,  as  in  the  case  of  combined  images  of  the 
same  object  producing  single  vision  ;  because,  in  the 
first  place,  the  two  objects  are  dissimilar,  and  therefore 
the  combination  is  not  perfect ;  and,  in  the  second  place, 
the  illusion  is  destroyed  by  the  existence  of  the  two 
other  uncombined  images.  We  next  try— 

2.  Similar  Objects.— If  the  two  objects,  the  images 
of  which  we  desire  to  combine,  are  exactly  similar,  then 
the  combined  image  will  be  exactly  like  a  natural  ob- 
ject. For  example : 

Experiment  1. — Place  two  pieces  of  money  of  the 
same  kind  on  the  table,  being  careful  that  the  stamped 
figures  shall  be  in  the  same  position.  Now,  looking 
down  upon  them,  combine  as  before.  Not  only  will 
the  outlines  of  the  two  pieces  combine,  but  the  stamped 
figures  in  the  minutest  details,  so  that  the  middle  com- 
bined binocular  image  will  have  all  the  appearance  of 
a  real  object.  This  is  illustrated  by  Figs.  37  and  38,  in 
which  the  position  of  parts  is  reversed,  because  the 
eyes  are  supposed  to  be  looking  down.  In  Fig.  37  the 
two  objects  (coins),  A  and  B^  are  combined  by  crossing 
the  eyes,  and  the  combined  or  binocular  opaque  image 
will  be  seen  at  the  point  of  sight  as  a'b,  while  monocular 
shadowy  images,  a  and  &',  will  be  seen  right  and  left. 
In  Fig.  38  the  combination  is  made  by  looking  beyond 
the  plane  of  the  coins,  and  the  coins  in  this  case  must 
not  be  more  than  an  interocular  space  apart.  The  com- 


SUPERPOSITION  OF  EXTERNAL  IMAGES. 


113 


bined  images,  like  a  real  opaque  object,  will  be  seen  at 
the  point  of  sight  abf,  and  the  two  shadowy  monocular 
images  right  and  left,  as  before,  only  they  are  now  het- 
eronymous. 


FIG.  37. 


FIG. 


ii> 


Iii  this  case,  though  the  combination  is  perfect,  yet 
the  illusion  is  still  not  complete,  because  of  the  presence 
of  the  accompanying  monocular  images ;  but  the  forma- 
tion of  these  may  be  prevented  by  the  use  of  appro- 
priate screens. 

Experiment  2. — If  in  the  first  experiment  with  the 
money,  before  combining,  we  hold  two  cards,  SG,  scf, 
Fig.  39,  one  in  either  hand  and  at  about  half  the  dis- 
tance to  the  table  (the  best  distance  is  the  plane  of  com- 
bination or  plane  of  sight,  for  then  there  will  be  no 
doubling  of  the  cards),  in  such  position  that  the  card 
in  the  right  hand,  sc,  will  hide  the  right  piece  A  from 
the  right  eye  but  not  from  the  left,  and  the  card  in  the 


114 


BINOCULAR  VISION. 


left  hand,  &/,  will  hide  the  left  piece  E  from  the  left 
eye  but  not  from  the  right,  and  then  make  the  com- 
bination by  crossing  the  eyes,  the  combined  binocular 
opaque  image  will  be  formed  as  before ;  but  the  mo- 
nocular images  will  not  appear,  because  there  will  be 


FIG.  39. 


FIG.  40. 


no  other  retinal  image  formed  except  on  the  central 
spots.  This  is  represented  in  Fig.  39.  In  case  we 
combine  beyond  the  plane  of  the  objects,  then  a  me- 
dian screen,  sc,  Fig.  40,  extending  from  the  root  of 
the  nose  n  to  the  table,  midway  between  the  objects, 
will  prevent  the  formation  of  the  monocular  images, 
as  shown. 

But  in  these  cases,  although  the  union  of  the  two 
images  is  perfect,  and  although  we  see  nothing  but  an 
apparently  solid  opaque  object,  even  yet  the  illusion  is 
not  absolute ;  partly  because  the  table  is  doubled  and 
therefore  unreal,  and  partly  because  the  eye  is  adjusted 
to  the  point  of  sight,  whereas  the  light  comes  from  the 


SUPERPOSITION   OF  EXTERNAL   IMAGES.  H5 

object,  which  is  either  nearer  as  in  Fig.  40,  or  farther 
off  as  in  Fig.  39,  than  that  point.  We  will  try  there- 
fore still  another  case. 

3.  Many  Similar  Objects  regularly  arranged.— The 
illusion  is  most  complete  when  we  combine  the  images 
of  many  similar  objects  regularly  arranged  over  the 
whole  field  of  view,  such  as  the  regular  figures  of  a 
tessellated  pavement  or  oilcloth,  or  of  a  regularly  fig- 
ured carpet  of  small  pattern,  or  of  a  papered  wall  of 
regular  pattern,  or  the  diamond-shaped  spaces  of  a  wire 
grating.  In  such  a  case,  when  by  convergence  we  com- 
bine two  contiguous  figures  immediately  in  front,  other 
contiguous  figures  all  over  the  plane  also  combine.  In 
other  words,  by  the  motion  of  the  eyes  in  opposite  di- 
rections in  convergence,  the  images  of  the  whole  plane 
of  the  figured  surface  are  slidden  by  one  eye  to  the  left 
and  by  the  other  eye  to  the  right,  until  combination 
takes  place  again  over  the  whole  field.  When  the  com- 
bination is  effected,  if  we  hold  the  point  of  sight  steady, 
the  combined  images  of  the  figures,  at  first  a  little 
blurred,  become  sharp  and  clear ;  and  then  the  whole 
figured  plane  comes  forward  to  the  point  of  sight,  and 
appears  there  as  distinctly  as  a  real  object,  but  on  a 
smaller  scale  in  proportion  to  the  less  distance.  This 
is  represented  in  Fig.  41,  in  which  the  strong  line  P  P 
represents  the  plane  of  the  regular  figures  1,  2,  3,  4,  5, 
etc.  When  contiguous  figures,  6  and  7,  are  united  by 
convergence  at  the  point  of  sight,  and  seen  there,  then 
all  other  contiguous  figures,  1  and  2,  2  and  3,  etc.,  all 
over  the  plane,  will  be  similarly  united,  and  the  whole 
plane  with  all  its  figures  will  advance  and  be  distinctly 
seen  at  the  distance  pf  p'.  When  by  stronger  conver- 
gence alternate  figures,  5  and  7,  are  combined  at  a  nearer 
point  of  sight  5  on  the  plane  p"  p" — or  (which  is  the 


116 


BINOCULAR  VISION. 


same)  when  we  use  the  plane  p'  p'  first  obtained  with 
all  its  figures  as  a  real  object,  and  again  combine  con- 
tiguous figures — the  whole  plane  advances  top" p" ,  and 
is  seen  as  a  distinct  object  with  a  still  smaller  pattern 
of  figures.  Using  the  plane  thus  obtained  again  as  an 
object,  and  uniting  its  contiguous  figures,  the  whole 


FIG.  41. 


plane  again  advances  still  nearer,  and  the  figures  be- 
come still  smaller  at  p'"  p'" .  In  this  manner  I  have 
often  distinctly  seen  a  regularly  figured  wall  or  pave- 
ment on  six  or  seven  different  planes  coming  nearer 
and  nearer,  and  becoming  smaller  and  smaller,  until  the 
nearest  was  within  3  inches  of  the  eyes,  and  the  figures 


SUPERPOSITION   OF  EXTERNAL  IMAGES.  H7 

in  exquisite  miniature,  and  yet  the  whole  so  apparently 
real  that  it  seemed  to  me  I  could  rap  my  knuckles 
against  the  wall  or  pavement.  When  thus  looking  at 
the  nearest  image,  by  a  slight  relaxation  of  convergence 
we  may  drop  the  image  and  catch  it  on  the  next  plane, 
and  again  drop  it  to  each  successive  plane,  until  it  falls 
to  its  natural  place. 

If  the  figures  of  the  pattern  are  not  larger  than  the 
distance  between  the  optic  centers  (2J  inches),  then  it 
is  possible  also  to  unite  the  figures  beyond  the  real  plane 
—i.e.,  on  the  plane  P1  P '.  In  this  case  the  figures  will 
be  proportionately  enlarged,  as  shown  by  the  diagram. 
But  it  is  difficult  by  this  method  to  make  the  image 
clear,  the  reason  for  which  we  shall  soon  see. 

In  ail  cases  of  illusive  images  the  head  ought  to  be 
held  steady.  If  it  be  moved  from  side  to  side  while 
gazing  at  such  an  image,  the  image  will  also  move  from 
side  to  side — in  the  same  direction  as  the  head  if  the 
point  of  sight  be  nearer  than  the  object,  and  in  the 
opposite  direction  if  the  point  of  sight  be  beyond  the 
object.  It  is  necessary  too,  in  all  experiments  on  com- 
bination of  images,  that  the  interocular  line  should  be 
exactly  parallel  with  the  line  joining  the  objects  to  be 
combined;  otherwise  one  image  will  be  higher  than 
the  other. 

Dissociation  of  Consensual  Adjustments.— We  have 
said  above  that  when  the  combination  in  case  3  (and  so 
also  in  the  other  cases)  is  first  obtained,  the  image  of  the 
figures  is  not  distinct,  but  afterward  becomes  clear  and 
sharp.  The  reason  is  this :  The  voluntary  adjustment 
of  the  optic  axes  (axial  adjustment)  to  a  nearer  distance 
than  the  object  carries  with  it,  by  consensus,  the  focal 
adjustment  and  pupillary  contraction  for  the  same  dis- 
tance. But  since  the  lenses  are  adjusted  for  a  nearer 


118  BINOCULAR  VISION. 

distance  than  the  object,  the  retinal  image  will  be  in- 
distinct. The  subsequent  clearing  of  the  image,  there- 
fore, is  the  result  of  a  dissociation  of  the  axial  and  focal 
adjustments.  The  optic  axes  are  adjusted  for  the  point 
of  sight  or  distance  of  the  illusive  image,  and  the  lenses 
are  adjusted  for  the  distance  of  the  object.  Some  per- 
sons do  not  iind  it  easy  to  make  this  dissociation,  and 
therefore  to  make  the  illusive  image  perfectly  clear. 
To  presbyopic  persons  it  is  not  difficult,  but  normal 
eyes  will  find  some,  though  not  insuperable,  difficulty. 

Now  it  becomes  an  interesting  question  :  When  the 
axial  and  focal  adjustments  are  thus  dissociated,  with 
which  one  does  the  pupillary  contraction  ally  itself  ?  I 
answer,  it  allies  itself  with  the  focal  adjustment.  This 
may  be  proved  as  follows : 

Experiment. — While  the  combination  and  the  forma- 
tion of  the  illusive  image  are  taking  place,  let  an  assist- 
ant standing  behind  observe  the  pupil  in  a  small  mirror 
suitably  placed  in  front  and  a  little  to  one  side  of  one 
eye.  He  will  see  that  at  first  the  pupil  contracts 
strongly,  associating  itself  with  the  axial  and  focal 
adjustments  to  the  point  of  sight ;  but  as  soon  as  the 
illusive  image  clears  and  becomes  distinct,  he  will  ob- 
serve that  the  pupil  has  enlarged  again. 

General  Conclusions. — It  is  evident,  therefore,  that 
the  combination  of  the  similar  images  of  two  different 
objects  may  produce  the  same  visual  effect  as  the  com- 
bination of  the  two  images  of  the  same  object.  In 
other  words,  single  vision,  or  ordinary  perception  of 
objects,  is  by  combination  of  two  similar  images ;  and 
it  makes  no  difference  whether  the  two  images  belong 
to  the  same  object  or  to  two  different  but  similar  ob- 
jects. This  idea  must  be  clearly  apprehended  and  held 
fast ;  otherwise  all  that  follows  will  be  unintelligible. 


SUPERPOSITION  OF  EXTERNAL  IMAGES.  H9 

Again,  it  is  evident  that  two  objects  may  be  seen  as 
one,  and,  contrariwise,  one  object  may  be  seen  as  two 
images.  We  see  then  the  absolute  necessity,  in  binoc- 
ular vision,  that  we  should  speak  of  seeing  only  external 
images,  the  signs  of  objects.  They  are  usually — i.  e., 
under  ordinary  conditions — the  true  signs,  but  often 
untrue,  deceptive,  illusory  signs. 


CHAPTEK  III. 

BINOCULA R   PERSPECTIVE. 

THUS  far  we  have  investigated  the  case  of  flat  ob- 
jects, or  of  figures  or  colored  spaces  on  a  plane.  We 
have  shown  how  the  images  of  these  may  be  combined 
at  pleasure,  so  as  to  give  the  illusory  appearance  of 
objects  or  figures  at  places  and  of  sizes  different  from 
their  real  places  and  sizes.  We  come  now  to  the  more 
complex  case  of  solid  objects  of  three  dimensions,  and 
of  objects  situated  at  different  distances.  This  brings 
us  to  the  important  subject  of  the  perception  of  depth 
of  space  so  far  as  this  is  connected  with  binocularity ; 
or,  in  other  words,  to  the  subject  of  binocular  perspec- 
tive. We  will  introduce  the  subject  with  some  simple 
experiments. 

Experiment  1. — Place  one  forefinger  before  the 
other  in  the  median  plane,  as  in  the  experiment  on 
page  94.  As  already  seen,  when  we  look  at  the  farther 
finger,  the  nearer  one  is  doubled  heteronymously  ;  when 
we  look  at  the  nearer  finger,  the  farther  one  is  doubled 
homonymously.  We  can  not  see  them  both  single  at 
the  same  time.  The  reason  is  obvious.  If  we  shut  one 
eye,  say  the  left,  we  see  the  fingers  as  in  Fig.  42,  I ;  if 
we  shut  the  right  eye,  we  see  them  as  in  Fig.  42,  II. 
Now  these  two  can  not  be  combined,  because  they  are 


BINOCULAR  PERSPECTIVE. 


121 


different.  When  we  combine  the  images  of  the  farther 
fingers,  a  and  #',  the  nearer,  b  and  £',  will  not  have  come 
together  yet,  and  will  therefore  be  heteronymously 


FIG.  43. 


FIG.  42. 


u 


R 


II 


double,  as  in  Fig.  43,  I ;  when  by  greater  convergence 
we  combine  the  images  b  and  bf  of  the  nearer  finger, 
then  the  images  a  and  a'  of  the  farther  will  have  crossed 
over  and  become  homonymously  double,  as  in  Fig.  43, 
II.  As  in  previous  experiments,  double  images  are 
given  in  dotted  outline,  and  left-eye  images  are  marked 
with  primed  letters,  and  combined  images  with  capitals. 

]Srow,  in  this  experiment  we  are  distinctly  conscious 
of  a  greater  convergence  of  the  optic  axes  necessary  to 
combine  the  double  images  of  the  nearer  finger,  and  of 
a  less  convergence  to  combine  the  double  images  of  the 
farther.  Thus  the  eyes  range  back  and  forth  by  greater 
and  less  convergence,  combining  the  double  images  of 
the  one  and  the  other,  or  transferring  the  point  of  sight 
from  one  to  the  other ;  and  thus  we  acquire  a  distinct 
perception  of  distance  between  the  two.  It  is  literally 
a  rapid  process  of  triangulation,  the  base-line  being  the 
interocular  distance. 

Experiment  2. — We  take  a  rod  about  a  foot  long, 
and  hold  it  in  the  median  plane  a  little  below  the  hori- 
zontal plane  passing  through  the  eyes,  so  that  we  can 
see  along  its  upper  edge,  the  nearer  end  about  six  or 


122  BINOCULAR  VISION. 

eight  inches  from  the  eyes.  If  now,  shutting  the  left 
eye,  we  observe  the  projection  of  the  rod  against  the 

wall,  it  will  be  like  this —  J  — a  being  the  nearer 
and  ~b  the  farther  end.  If  we  shut  the  right  eye  and 
open  the  left,  the  projection  will  be  like  this—  ^  ,. 

These  lines  are  exactly  like  the  retinal  images  formed 
by  the  rod  in  the  right  and  left  eyes  respectively,  ex- 
cept that  these  images  are  inverted.  Or,  to  express  it 
differently,  these  lines  would  make  images  on  the  right 
and  left  retinae  respectively  exactly  like  those  made  by 
the  rod ;  they  are  the  facsimiles  of  the  external  images 
of  the  rod.  If  we  now  open  both  eyes  and  fix  attention 
on  the  farther  end,  then  the  nearer  end  will  be  seen 
double  heteronymously,  and  the  projection  will  be 

B 
thus —     /\     .     If,  on  the  contrary,  we  look   at   the 

a/    \a' 

nearer  end,  .then  this  of  course  will  be  single,  but  the 
farther  end  will  now  be  double  homonymously,  and 

&'\   /& 
the  projection  will  be  thus —     \/     .     If,  finally,  we 

A 

look  at  the  middle  point,  this  point  will  of  course  be 
seen  single,  but  both  ends  double,  the  one  homony- 
mously, the  other  heteronymously,  and  the  projection 

will  be  thus—     V    .     Or,  to  put  it  differently,  the 

external  images  of  the  two  eyes  are  like  these  lines — 

/       and       \     :  if  these  two  be  brought  together  so 

as  to  unite  the  farther  ends  5  ~b ',  then  by  greater  con- 
vergence the  middle  points,  and  then  by  still  greater 
convergence  the  nearer  ends  a  a' ',  the  three  projections 
above  given  are  obtained ;  but  it  is  obviously  impossi- 
ble to  unite  all  parts  and  see  single  the  whole  rod  at 


BINOCULAR  PERSPECTIVE.  123 

once.  'Now,  if  we  observe  attentively,  we  find  that  in 
looking  at  the  rod  the  eyes  range  back  and  forth  by 
greater  or  less  convergence,  uniting  successively  the 
different  parts,  and  thus  acquire  a  distinct  perception 
of  the  difference  of  distance  or  depth  of  space  between 
the  nearer  and  the  farther  end. 

Experiment  3. — We  take  next  a  small  thin  book, 
and  hold  it  as  before  six  to  eight  inches  distant  in  the 
median  plane,  a  little  below  the  horizontal  plane  of 
sight,  so  that  the  back  and  the  upper  edge  are  visible. 
If  we  shut  the  left  eye,  we  see  the  back,  the  upper  edge, 

and  the  whole  right  side,  thus —  fa  .     The  retinal  image 

formed  in  the  right  eye  is  exactly  like  this  figure,  except 
that  it  is  inverted ;  this  figure  makes  exactly  the  same 
retinal  image  as  the  book  does  in  the  right  eye ;  it  is 
the  facsimile  of  the  external  image  of  the  book  for  the 
right  eye.  If  we  shut  the  right  eye  and  open  the  left, 
we  see  the  back,  the  upper  edge,  and  the  whole  left 

side,  thus—  IB.     Now,  if  we  open  both  eyes,  we  must 

and  do  see  both  these  images.  If  we  look  beyond  the 
book,  the  two  images  are  wholly  separated,  thus — 

H.    If  we  look  at  the  farther  part,  we  bring  these 

two  images  together  so  as  to  unite  the  farther  part  and 
see  it  single,  but  the  nearer  part  or  back  is  double, 

thus — (pi.  If  we  look  at  the  nearer  part  or  back, 
then  this  is  seen  single,  but  the  farther  edge  is  now 
double,  thus —  n.  But  by  no  effort  is  it  possible  to 
see  it  single  in  all  parts  at  the  same  time,  because  these 


124:  BINOCULAR   VISION. 

dissimilar  external  images  can  not  be  wholly  united. 
The  eyes  therefore  range  rapidly  back  and  forth,  suc- 
cessively uniting  different  parts  by  greater  and  less 
convergence,  and  thus  acquire  a  distinct  perception  of 
distance  between  the  back  and  front,  and  hence  of  depth 
of  space. 

After  these  simple  illustrations  we  are  now  prepared 
to  generalize.  It  is  evident  that  solid  objects  as  seen 
by  two  eyes  form  different  mathematical  projections, 
and  therefore  form  different  retinal  images  in  the  two 
eyes,  and  therefore  also  different  external  images. 
Hence  the  images  of  the  same  object,  whether  retinal 
or  external,  formed  by  the  two  eyes,  are  necessarily 
dissimilar  if  the  object  occupies  considerable  depth  of 
space.  But  dissimilar  images  can  not  be  united  wholly  : 
for  when  by  stronger  convergence  we  unite  the  nearer 
parts,  the  farther  will  be  double ;  and  when  by  less 
convergence  we  unite  the  farther  parts,  the  nearer  will 
be  double.  Therefore  the  eyes  run  rapidly  and  uncon- 
sciously back  and  forth,  uniting  successively  different 
parts,  and  thus  acquire  the  perception  of  depth  of 
space  occupied  by  the  object.  But  what  is  true  of  a 
single  object  is  true  of  different  objects  placed  one  be- 
yond the  other,  as  the  two  fingers  in  experiment  1,  page 
120.  We  can  not  at  the  same  time  unite  nearer  and 
more  distant  objects,  but  the  point  of  sight  runs  rapidly 
and  unconsciously  back  and  forth,  uniting  them  succes- 
sively, and  thus  we  acquire  a  perception  of  depth  of  space 
lying  between  them.  Therefore,  the  perception  of  the 
third  dimension,  viz.,  depth  or  relative  distance,  whether 
in  a  single  object  or  in  a  scene,  is  the  result  of  the  suc- 
cessive combination  of  the  different  parts  of  the  two 
dissimilar  images  of  the  object  or  the  scene:  dissimilar, 
because  taken  from  different  points,  viz.,  the  two  eyes 


BINOCULAR  PERSPECTIVE.  125 

with  the  interocular  distance  between.  This  funda- 
mental proposition  will  be  slightly  modified  in  our 
chapter  on  the  theory  of  binocular  perspective.  In  the 
mean  time  it  must  be  clearly  conceived  and  held  fast ; 
otherwise  all  that  follows  on  stereoscopy  will  be  unin- 
telligible. 


STEREOSCOPV. 

"We  have  already  seen  (page  96)  that  in  binocular 
vision  we  see  objects  single  by  a  combination  of  two 
similar  or  nearly  similar  images,  and  that  therefore 
(page  118)  it  makes  no  difference  whether  the  images 
are  those  of  the  same  object  or  of  different  objects,  if 
the  images  in  the  two  cases  are  identical,  and  if  wre  take 
care  to  cut  off  the  monocular  images  which  are  formed 
in  the  latter  case.  Hence,  if  we  draw  two  pictures  of 
a  rod  in  the  two  positions  shown  in  Fi^  44 

Fig.  44,  and  then  combine  them  by 
converging  the  eyes,  taking  care  to  cut 
off  the  monocular  images  as  directed  on 
page  114,  Fig.  39,  the  visual  result  will 
be  exactly  the  same  as  that  of  an  actual 
rod  in  the  median  line ;  and  therefore  it  will  look  like 
such  a  rod.  As  in  the  case  of  the  actual  rod,  by  greater 
or  less  convergence  of  the  optic  axes  we  may  combine 
successively  different  parts  ;  and  the  eyes  therefore  seem 
to  run  back  and  forth,  and  we  have  a  distinct  perception 
of  depth  of  space.  To  produce  the  proper  effect,  the 
two  pictures  of  Fig.  44  ought  to  be  combined  at  a  dis- 
tance of  not  more  than  six  or  eight  inches 

So  also  in  the  case  of  the  book,  page  123.  If  we 
exactly  reverse  the  case  described  there— i.  e.,  if  we 


126  BINOCULAR  VISION. 

make  two  pictures  of  a  book  as  seen  by  one  eye  and 
the  other,  and  then  combine  them,  cutting  off  the  mo- 
nocular images— we  have  the  exact  appearance  of  an 
actual  solid  book.  The  only  reason  why  the  illusion  is 
not  complete  is,  that  there  are  other  kinds  of  perspec- 
tive besides  the  binocular ;  and  in  this  case  especially  be- 
cause there  is  not  the  same  change  of  focal  adjustment 
necessary  for  distinct  image  as  in  the  case  of  a  real 
object. 

Now  this  is  the  principle  of  the  stereoscope.  The 
stereoscope  is  an  instrument  for  facilitating  the  com- 
bination of  two  such  pictures,  and  at  the  same  time 
cutting  off  the  uncombined  monocular  images  which 
would  tend  to  destroy  the  illusion. 

Stereoscopic  Pictures.— When  we  look  at  an  object 
having  considerable  depth  in  space,  or  at  a  scene,  there 
is  an  image  of  the  object  or  scene  formed  on  each  retina. 
These  two  images  are  not  exactly  alike,  because  they 
are  taken  from  different  points  of  view.  Now  suppose 
we  draw  two  pictures  exactly  like  these  two  retinal 
images,  except  inverted.  Obviously  these  two  pictures 
will  make  images  on  the  corresponding  retinae  exactly 
like  those  made  by  the  original  object  on  the  one  retina 
and  the  other,  and  therefore  will  be  exactly  like  this 
object  seen  by  one  eye  and  then  by  the  other.  Now, 
we  have  seen  the  wonderful  similarity  of  the  eye  to  a 
photographic  camera.  Suppose,  then,  instead  of  draw- 
ing the  pictures  like  the  two  retinal  images,  we  photo- 
graph them.  Two  cameras  are  placed  before  an  object 
or  a  scene  with  a  distance  between  of  two  or  three  feet. 
They  are  like  two  great  eyes  with  large  interocular 
space.  The  sensitive  plate  represents  the  retina,  and 
the  pictures  the  retinal  images.  The  photographic 
pictures  thus  taken  can  not  be  exactly  alike,  because 


BINOCULAR  PERSPECTIVE.  127 

taken  from  different  points.  They  will  differ  from 
each  other  exactly  as  the  two  retinal  images  of  the  same 
object  or  scene  differ,  only  certainly  in  a  greater  degree. 
Therefore,  if  these  two  photographs  be  binocularly 
combined  as  in  the  experiments  previously  given,  they 
ought  to  and  must  produce  a  visual  effect  exactly  like 
an  actual  object  or  scene ;  for  in  looking  at  an  object 
or  scene,  we  are  only  combining  retinal  images  (or  their 
external  representatives)  exactly  like  these  pictures,  be- 
cause taken  in  the  same  way. 

This  is  substantially  the  manner  in  which  stereo- 
S3Opic  pictures  are  taken.  It  is  not  always  necessary, 
indeed,  to  have  two  Cameras ;  for  the  pictures,  being 
permanent  and  not  evanescent  like  retinal  images,  may 
be  retained  and  combined  at  any  time.  The  object  or 
scene  is  often  photographed  from  one  position,  and 
then  the  camera  is  moved  a  little,  and  the  same  object 
or  scene  is  again  photographed  from  the  new  position. 
The  two  slightly  dissimilar  pictures  thus  taken  are  then 
mounted  in  such  wise  that  the  right-hand  picture  shall 
be  that  taken  by  the  right  camera,  and  the  left-hand 
picture  that  taken  by  the  left  camera.  In  other  words, 
they  are  mounted  so  that  the  right  picture  shall  be 
similar  (except  inverted)  to  the  retinal  image  of  the 
object  or  scene  in  the  right  eye,  and  the  left  picture 
to  the  retinal  image  in  the  left  eye.  The  marvelous 
distinctness  of  the  perception  of  depth  of  space,  and 
therefore  the  marvelous  resemblance  to  an  actual  object 
or  scene,  produced  by  binocular  combination  of  such 
pictures  properly  taken  and  properly  mounted,  is  well 
known. 

It  is  easy  to  test  whether  stereoscopic  pictures  are 
properly  mounted  or  not.  Seleet  some  point  or  object 
in  the  foreground ;  measure  accurately  with  a  pair  of 


128  BINOCULAR  VISION. 

dividers  the  distance  between  it  and  the  same  point  or 
object  in  the  other  picture  ;  compare  this  with  the  dis- 
tance between  identical  points  in  the  extreme  back- 
ground of  the  two  pictures.  The  distance  in  the  latter 
case  ought  to  be  greater  than  in  the  former.  This  is 
the  proper  mounting  for  viewing  pictures  in  a  stereo- 
scope. If  they  are  to  be  combined  with  the  naked  eye, 
then  the  reverse  mounting  is  better. 

Combination  of  Stereoscopic  Pictures.— Stereoscopic 
pictures  may  be  easily  combined  by  the  use  of  the  ste- 
reoscope or  with  the  naked  eyes.  For  inexperienced 
persons,  however,  the  latter  is  more  difficult  and  the 
illusion  less  complete,  unless  with  special  precautions. 
Nevertheless,  it  will  be  best  to  begin  with  this  method, 
because  the  principles  involved  are  thus  most  easily 
explained. 

Combination  with  the  Naked  Eyes, — In  combining 
stereoscopic  pictures  with  the  naked  eyes,  there  are  two 
difficulties  in  the  way  of  obtaining  the  best  results. 
First,  it  is  evident  that  such  pictures,  as  usually  mount- 
ed, were  intended  to  be  combined  beyond  the  plane  of 
the  card;  for  it  is  only  thus  that  the  object  or  scene 
can  be  seen  in  natural  perspective,  and  of  natural  size, 
and  at  natural  distance.  But  in  thus  combining,  the 
eyes  are  of  course  looking  at  a  distant  object,  and  con- 
sequently parallel  or  nearly  so.  The  eyes  are  therefore 
focally  adjusted  for  a  distant  object,  but  the  light  comes 
from  a  very  near  object,  viz.,  the  card-pictures.  Hence, 
although  the  pictures  unite  perfectly,  the  combined 
image  or  scene  is  indistinct.  Myopic  eyes  will  not  ex- 
perience this  difficulty,  and  in  normal  eyes  it  may  be 
remedied  by  the  use  of  slightly  convex  glasses.  Such 
glasses  supplement  the  lenses  of  the  eye,  and  make 
clear  vision  of  a  near  object  when  the  eyes  are  really 


BINOCULAR   PERSPECTIVE.  129 

looking  far  away;  or,  in  other  words,  make  a  clear 
image  of  a  near  object  on  the  retina  of  the  unadjusted 
eye. 

Another  difficulty  is,  that  the  pictures  are  usually  so 
mounted  that  identical  points  are  farther  apart  than  the 
interocular  distance,  and  therefore,  even  with  the  optic 
axes  parallel — i.  e.,  looking  at  an  infinite  distance — the 
pictures  do  not  combine.  This  difficulty  is  easily  re- 
moved by  cutting  down  the  inner  edges  of  the  two  pic- 
tures, in  order  to  bring  them  a  little  nearer  together,  so 
that  identical  points  in  the  background  shall  be  equal 
to  or  a  little  less  than  the  interocular  distance.* 

With  this  explanation  we  now  proceed  to  give  ex. 
amples  of  naked-eye  combination. 

Fig.  45  represents  a  projection  of  a  skeleton  trun- 
cated cone  made  of  wire,  as  seen  from  two  positions  a 
little  separated  from  each  other ;  in  other  words,  as  they 

FIG.  45. 


would  be  taken  by  two  cameras  for  a  stereoscopic  card ; 
or,  again,  as  they  would  be  taken  on  the  retinae  of  two 
eyes  looking  at  such  a  skeleton  truncated  cone  with  the 
smaller  end  toward  the  observer. 

Experiment. — If  wTe  now  place  a  median  screen  10 
inches  or  a  foot  long  midway  between  these  two  figures, 

*  In  a  subsequent  chapter  we  give  the  method  of  determining  with 
accuracy  the  interocular  distance. 


130  BINOCULAR  VISION, 

A  and  B,  and  place  the  nose  and  middle  of  forehead 
against  the  other  edge  of  the  screen,  so  that  the  right 
eye  can  only  see  A  and  the  left  eye  J3 — assisting  the 
eye  with  slightly  convex  glasses  if  necessary — and  then 
gaze  as  it  were  at  a  distant  object  beyond  the  plane  of 
the  picture,  the  two  figures  will  be  seen  to  approach 
and  finally  to  unite  in  one,  and  appear  as  a  real  skeleton 
truncated  cone  of  a  considerable  height.  If  we  are  able 
to  analyze  our  visual  impressions,  we  shall  find  further 
that,  when  we  look  steadily  at  the  larger  circle  or  base, 
the  smaller  cone  or  summit  is  slightly  double,  and  when 
we  look  steadily  at  the  smaller  circle  or  summit  this  be- 
comes single,  but  now  the  larger  circle  or  base  is  double ; 
further,  that  it  requires  a  greater  convergence,  as  in 
looking  at  a  nearer  object^  to  unite  the  smaller  circles, 
and  a  less  convergence,  as  in  looking  at  a  more  distant 
object,  to  unite  the  larger  circles ;  and  still  further,  that 
the  lines  a  a!  and  Z>  b'  behave  exactly  like  the  lines  de- 
scribed on  page  122,  forming  a  V,  an  inverted  V,  or  an 
X,  according  to  the  distance  of  the  point  of  sight ;  or, 
in  other  words,  behave  exactly  like  the  two  images  of 
a  rod  held  in  the  median  plane  with  one  end  nearer 
than  the  other.  In  a  single  word,  the  phenomena  are 
exactly  those  produced  by  looking  at  an  actual  skeleton 
cone  made  of  wires.  Thus,  as  in  the  case  of  an  actual 
object,  the  eyes  by  greater  and  less  convergence  run 
their  point  of  sight  back  and  forth,  uniting  different 
parts,  and  thus  acquire  a  distinct  perception  of  depth 
of  space  between  the  smaller  and  larger  circles. 

The  same  is  true  of  all  pictures  constructed  on  this 
principle,  and  all  objects  or  scenes  on  stereoscopic  cards. 
In  these,  it  will  be  remembered,  identical  points  in  the 
foreground  are  always  nearer  together  than  identical 
points  in  the  background ;  therefore,  when  the  back- 


STEREOSCOPY. 


131 


ground  is  united  the  foreground  is  double,  and  vice 
versa.  We  may  represent  these  facts  diagrammatical!)7 
by  Fig.  46,  in  which  p  p  is  the  plane  of  the  pictures ; 
ms,  the  median  screen  resting  on  the  root  of  the  nose,  n  ; 
It  and  Z,  the  right  and  left  eyes. 
On  the  plane  of  the  paper  p  p,  a  FlG- 46- 

and  a'  represent  identical  points  in 
the  foreground,  viz.,  the  centers  of 
the  small  circles  in  the  diagram  Fig. 
45 ;  and  b  and  If  identical  points  in 
the  background  (centers  of  the  larger 
circles  in  Fig.  45).  Now  when  the 
eyes  are  directed  toward  b  and  b', 
the  two  visual  lines  will  pass  through 
these  points,  and  the  images  of  these 
two  points  will  fall  on  corresponding 
points  of  the  retinae,  viz.,  on  the  cen- 
tral spots,  and  will  be  united  and  seen 
.single.  But  where  ?  Manifestly  at 
the  point  of  optic  convergence  or  point 
of  sight  B.  ISTow  when  b  and  bf  fall 
on  corresponding  points  and  are  seen 
single,  evidently  a  and  a'  must  fall  on 
non-corresponding  points,  viz.,  the  two  temporal  por- 
tions of  the  retinae,  and  are  therefore  seen  double. 
When,  on  the  other  hand,  by  greater  convergence  the 
optic  axes  are  turned  on  a  and  a',  then  the  images 
of  these  fall  on  the  central  spots,  and  are  seen  single 
at  the  nearer  point  of  sight  A  ;  but  now  b  and  bf  are 
seen  double,  because  they  fall  on  non-corresponding 
points,  viz.,  the  two  nasal  halves  of  the  retinae.  Inter- 
mediate points  between  the  background  and  foreground 
will  be  seen  at  intermediate  points  between  B  and 
A.  Thus  the  point  of  sight  runs  back  and  forth  from 


132  BINOCULAR  VISION. 

background  £  to  foreground  A,  and  we  acquire  a 
distinct  perception  of  depth  of  space  between  these 
two  points. 

But,  for  those  at  all  practiced  in  binocular  experi- 
ments, by  far  the  most  perfect  naked-eye  combination 
is  obtained  by  crossing  the  eyes ;  i.  e.,  by  combining 
on  the  nearer  instead  of  the  farther  side  of  the  pictures. 
For  this  purpose,  however,  it  is  necessary  that  the 
mounting  be  reversed ;  i.  e.,  the  right-hand  picture 
must  be  put  on  the  left  side,  and  the  left-hand  pic- 
ture on  the  right  side  of  the  card.  By  this  reversal  it 
is  evident  that  identical  points  in  the  background  of 
the  two  pictures  are  nearer  together  than  identical 
points  in  the  foreground. 

If,  now,  holding  such  a  card  before  us  at  any  con- 
venient distance,  say  18  inches  or  2  feet,  we  converge 
the  optic  axes  so  that  the  right  eye  shall  look  across 
directly  toward  the  left  picture,  and  the  left  eye  toward 
the  right  picture,-  then  the  two  pictures  will  unite  at  the 
point  of  crossing  of  the  optic  axes  (point  of  sight),  and 
will  be  seen  there  in  exquisite  miniature,  but  with  per- 
fect perspective.  The  effect  is  really  marvelously  beau- 
tiful. For  persons  of  slightly  presbyopic  eyes  there  will 
be  no  difficulty  in  getting  the  combined  image  perfectly 
clear.  In  normal  eyes,  as  already  explained  (page  117), 
there  must  be  dissociation  between  the  axial  and  focal 
adjustments  before  the  combined  image  is  perfectly 
clear.  For  those  who  can  not  make  this  dissociation  it 
may  be  necessary  to  use  very  slightly  concave  glasses. 
Again,  if  the  observer  is  annoyed  by  the  existence  of 
the  monocular  uncombined  images  to  the  right  and 
left,  it  will  be  best  to  use  two  side  screens,  as  already 
explained  (page  114),  instead  of  the  median  screen  used 
in  combining  beyond  the  plane  of  the  picture. 


BINOCULAR   PERSPECTIVE.  133 

Experiment. — I  draw  (Fig.  47)  two  projections  of  a 
skeleton  truncated  cone  precisely  like  those  represented 
on  page  129,  but  reversed.  It  is  seen,  for  example,  that 
the  centers  of  the  small  circles  are  in  this  case  farther 

FIG.  47. 


apart  than  the  centers  of  the  large  circles.  If,  now, 
holding  these  about  18  inches  distant,  I  combine  them 
by  crossing  the  optic  axes,  the  impression  of  a  skeleton 
truncated  cone  with  the  smaller  end  toward  me  is  as 
complete  as  possible.  The  singleness  of  the  impression 
at  first  seems  perfect,  but  by  observing  attentively  the 
lines  a  and  a!  it  will  be  seen  that  they  unite  only  in 
points  and  not  throughout — that  they  come  together  as 
a  v,  thus — V,  or  an  inverted  v — A>  or  an  x — x>  according 
to  the  distance  of  the  point  of  sight.  In  other  words, 
when  by  greater  convergence  the  small  circle  is  sin- 
gle, the  larger  circle  is  double ;  and  when  by  less 
convergence  the  larger  circle  is  single,  then  the  small- 
er circle  is  double.  And  thus  the  eyes  run  the  point 
of  sight  back  and  forth,  uniting  first  the  one  and 
then  the  other,  and  in  this  way  acquire  a  clear  concep- 
tion of  depth  of  space  between  the  smaller  and  larger 
circles. 

These  facts  are  illustrated  by  the  diagram  Fig.  48, 
in  which,  as  before,  R  and  Z  are  the  two  eyes ;  n,  the 
root  of  nose  ;  P  P,  the  plane  of  the  pictures  ;  a  and  a'. 


134 


BINOCULAR  VISION. 


FIG.  48. 


identical  points  of  the  foreground,  and  b  and  I'  of  the 
background  ;  and  sc  and  «?',  the  two  side-screens  to  cut  off 

monocular  images.  When 
the  eyes  are  directed  toward 
a  and  a' ',  these  unite  and 
are  seen  at  the  point  of 
sight  as  a  single  object  A. 
When  the  eyes  by  less  con- 
vergence are  directed  to  5 
and  5',  then  these  are  seen 
single  at  the  point  of  sight 
B.  The  point  of  sight  runs 
back  and  forth  from  A  to 
B,  and  we  thus  acquire  dis- 
tinct perception  of  depth  of 
space  between. 

Of  course,  any  stereo- 
scopic pictures  may  be  com- 
bined in  this  way  if  we  re- 
verse the  mounting;  and  I 
am  quite  sure  that  any  one  who  will  try  it  will  be  de- 
lighted with  the  beautiful  miniature  effect  and  the  per- 
fection of  the  perspective. 

Combination  by  the  Use  of  the  Stereoscope. — The  stere- 
oscope is  an  instrument  for  facilitating  binocular  combi- 
nations beyond  the  plane  of  the  pictures.  By  means  of 
lenses  also  it  supplements  the  lenses  of  the  eyes,  and 
thus  makes  on  the  retinae  perfect  images  of  a  near  ob- 
ject, although  the  eyes  are  looking  at  a  distant  object, 
and  are  therefore  unadjusted  for  a  near  one.  The  lenses 
also  enlarge  the  images,  acting  like  a  perspective  glass, 
and  thus  complete  the  illusion  of  a  natural  scene  or 
object. 

It  is  difficult  to  convince  many  persons  that  there 


BINOCULAR  PERSPECTIVE.  135 

is  in  the  stereoscope  any  doubling  of  points  in  the  fore- 
ground when  the  background  is  regarded,  and  vice  versa. 
But  such  is  really  always  the  fact;  and  if  we  do  not 
observe  it,  it  is  because  we  have  not  carefully  analyzed 
our  visual  impressions.  It  is  best  observed  in  skeleton 
diagrams  of  geometrical  figures,  such  as  are  commonly 
used  to  explain  the  principles  of  stereoscopy.  In  or- 
dinary stereoscopic  pictures  it  is  also  easily  observed  in 
those  cases  where  points  in  the  extreme  foreground 
and  background  are  in  the  same  range ;  as,  for  example, 
when  a  column  far  in  front  is  projected  against  a  build- 
ing. In  such  a  case,  when  we  look  at  the  building  the 
column  is  distinctly  double,  and"  vice  versa.  For  my- 
self, I  never  look  at  a  stereoscopic  card,  whether  in  a 
sterescope  or  by  naked-eye  combination,  without  dis- 
tinctly observing  this  doubling.  For  example :  I  now 
combine  in  a  stereoscope  the  stereoscopic  pictures  of  a 
skeleton  polyhedron.  The  illusion  of  a  polyhedral  space 
inclosed  by  white  lines  is  perfect.  Now,  when  I  look  at 
the  farther  inclosing  lines  I  see  the  nearer  ones  double, 
and  vice  versa.  Moreover,  I  perceive  that  this  doubling 
is  absolutely  necessary  to  the  stereoscopic  effect,  for  it 
is  exactly  like  what  would  take  place  if  I  were  looking 
at  an  actual  skeleton  polyhedron. 

Inverse  Perspective. — I  have  heard  a  few  persons 
declare  that  they  saw  no  superiority  of  a  stereoscope 
over  an  ordinary  enlarging  or  perspective  glass ;  that 
they  saw  just  as  well  while  looking  through  the  stereo- 
scope if  they  shut  one  eye  as  with  both  eyes  open. 
Such  persons  evidently  do  not  combine  properly  the 
two  pictures,  and  they  lose  a  real  enjoyment.  That  the 
binocular  is  a  real  perspective,  entirely  different  from 
other  kinds,  may  be  clearly  demonstrated  by  the  phe- 
nomena of  inverse  perspective  now  about  to  be  described. 


136 


BINOCULAR   VISION. 


If  stereoscopic  diagrams  suitably  mounted  for  view- 
ing in  a  stereoscope  be  combined  with  the  naked  eye 
by  squinting  (crossing  the  optic  axes),  as  in  Fig.  48 
(page  134).  or  if  such  diagrams  properly  mounted  for 


BINOCULAR   PERSPECTIVE. 


137 


combination  by  squinting  be  viewed  in  the  stereoscope, 
the  perspective  is  completely  reversed,  the  background 
becoming  the  foreground,  and  vice  versa.  For  example, 
Fig.  49  represents  a  stereoscopic  card.  When  the  two 


138  BINOCULAR  VISION. 

pictures  are  combined  with  a  stereoscope,  the  result  is 
a  jelly-mold  with  the  small  end  toward  the  observer ; 
but  if  the  same  be  combined  with  the  naked  eye  by 
squinting,  we  have  now  beautifully  shown  the  same 
jelly-mold  reversed,  and  we  are  looking  into  the  hol- 
low. If  there  should  be  other  forms  of  perspective 
strongly  marked  in  the  pictures,  these  may  even  be 
overborne  by  the  inverse  binocular  perspective.  For 
example,  in  the  stereoscopic  picture  Fig.  50,  represent- 
ing the  interior  of  a  bridgeway,  the  diminishing  size  of 
the  arches  and  the  converging  lines,  even  without  the 
stereoscope,  at  once  by  mathematical  perspective  sug- 
gest the  interior  of  a  long  archway.  This  impression 
is  greatly  strengthened  by  viewing  it  in  the  stereoscope ; 
for  the  binocular  perspective  and  the  mathematical  per- 
spective strengthen  each  other,  and  the  illusion  is  com- 
plete. But  if  we  combine  these  with  the  naked  eyes 
by  squinting,  we  see  with  perfect  distinctness,  not  a 
long  hollow  archway,  the  small  arch  representing  the 
farther  end,  but  a  short  conical  solid,  with  the  small 
end  toward  the  observer.  Thus  the  binocular  perspec- 
tive entirely  overbears  the  mathematical. 

The  cause  of  this  reversal  of  the  natural  perspective 
is  shown  in  the  following  diagrams.  In  Fig.  51  the 
mounting  is  reversed,  as  seen  by  the  fact  that  the  points 
b  and  bf  in  the  background  are  nearer  together  than  the 
points  a  and  a'  in  the  foreground.  By  combining  these 
in  a  stereoscope,  the  background  is  seen  nearer  the  ob- 
server at  B,  and  the  foreground  thrown  farther  back 
to  A.  In  Fig.  52  the  pictures  are  mounted  suitably 
for  viewing  in  the  stereoscope,  but  are  combined  by 
the  naked  eye.  Here  also  the  perspective  is  reversed, 
for  the  background  is  seen  at  a  nearer  point  J?,  and  the 
foreground  at  a  farther  point  A. 


BINOCULAR  PERSPECTIVE. 


139 


This  inverse  perspective  is  easily  brought  out,  not 
only  in  stereoscopic  diagrams,  but  in  nearly  all  stereo- 
scopic pictures,  even  in  those  representing  extensive  and 


FIG.  51. 


FIG.  52. 


complex  views.  In  these,  of  course,  when  viewed  in 
the  stereoscope,  the  binocular  is  in  harmony  with  other 
forms  of  perspective,  and  each  enhances  the  effect  of 
the  other.  But  if  we  combine  with  the  naked  eyes  by 
squinting,  or  if  we  reverse  the  mounting  and  view  again 
with  the  stereoscope,  there  is  in  either  case  a  complete 
discordance  between  the  binocular  and  other  forms  of 
perspective.  In  some  cases  the  ordinary  perspective  is 
too  strong  for  the  binocular,  and  the  only  result  is  a 
kind  of  confusion  of  the  view ;  but  in  others  the  binoc- 
ular completely  overbears  all  opposition  and  reverses 
the  perspective,  often  producing  the  strangest  effects. 


140  BINOCULAR   VISIOX. 

For  example,  I  now  take  up  a  stereoscopic  card  ^pre- 
senting a  building  with  extensive  grounds  in  front.  I 
view  it  in  a  stereoscope.  The  natural  perspective  comes 
out  beautifully — the  fine  building  in  the  background, 
the  sloping  lawn  in  the  middle,  and  a  piece  of  statuary 
and  a  fountain  in  the  foreground.  I  now  combine  the 
same  with  the  naked  eyes  by  squinting.  As  soon  as 
the  combination  is  perfect  and  the  vision  distinct,  the 

house  is  seen  in  front,  and 
through  a  space  in  the  wall 
the  statue  and  fountain  are 
seen  behind.  Observing 
more  closely,  all  the  parts 
of  the  house,  the  slope  of 
the  roof,  and  the  slope  of 
the  lawn  are  also  reversed. 
In  Fig.  53,  A  and  B  show 
the  natural  and  the  inverted 
perspective  in  section,  and 
the  arrows  the  direction  in  which  the  observer  is  look- 
ing. In  the  one  case  the  roof  and  the  lawn  slope  down- 
ward and  toward  the  observer ;  in  the  other,  downward 
and  away  from  the  observer.  In  the  one  case  the  build- 
ing is  a  solid  object;  in  the  other  it  is  an  inverted  shell, 
and  we  are  looking  at  the  interior  of  the  shell. 

In  nearly  all  stereoscopic  views  I  can  thus  invert 
the  perspective  by  naked-eye  combination.  Almost 
the  only  exceptions  are  views  looking  up  the  streets  of 
cities.  Here  the  mathematical  perspective  is  too  strong 
to  be  overborne.  Stereoscopic  pictures  of  the  full  moon 
are  quite  common.  If  these  be  viewed  in  a  stereoscope, 
we  have  the  natural  perspective,  viz.,  the  appearance  of 
a  globe  ;  if  combined  with  the  naked  eyes  by  squinting, 
we  have  a  hollow  hemisphere.  If  the  mounting  be 


BINOCULAR   PERSPECTIVE. 

reversed,  then  the  hollow  is  seen  in  the  stereoscope  and 
the  solid  globe  with  the  naked  eyes.  We  will  give  one 
more  example.  I  have  now  a  stereoscopic  view  of  the 
city  of  Paris,  but  not  looking  up  the  streets.  When 
viewed  in  the  stereoscope,  the  perspective  is  natural 
and  perfect;  the  large  houses  are  in  the  foreground 
and  below,  and  the  others  gradually  smaller  and  higher, 
until  the  dimmest  and  smallest  are  on  the  uppermost 
part  and  form  the  distant  background.  I  am,  looking 
on  the  upper  surface  of  a  receding  rising  plane  full  of 
houses.  I  now  combine  the  same  pictures  with  the 
naked  eyes  by  squinting.  As  soon  as  the  combined 
image  comes  out  clear,  1  see  the  smallest  and  dimmest 
houses  on  the  upper  part  of  the  scene,  but  nearest  to 
me.  I  am  looking  on  the  under  side  of  a  receding 
declining  plane,  on  which  the  houses  grow  larger  and 
larger  in  the  distance,  until  they  become  largest  at  the 
lowest  and  farthest  margin  of  the  plane.  If  the  mount- 
ing of  the  pictures  be  reversed,  then  the  natural  per- 
spective will  be  seen  with  the  naked  eyes,  and  the  in- 
verse perspective  just  described  will  be  seen  in  the 
stereoscope. 

The  extreme  accuracy  of  our  judgment  of  relative 
distance  by  binocular  perspective  is  well  shown  by  the 
combination,  either  by  the  naked  eyes  or  by  the  stereo- 
scope, of  apparently  identical  figures  on  a  flat  plane. 
For  example,  in  combining  with  the  naked  eyes  the 
figures  of  a  regularly  figured  wall-paper  or  tessellated 
pavement,  the  least  want  of  perfect  regularity  in  the 
size  or  position  of  the  figures  is  at  once  detected  by 
an  appearance  of  gentle  undulations  or  more  abrupt 
changes  of  level.  This  fact  is  made  use  of  in  detect- 
ing counterfeit  notes.  If  two  notes  from  the  same 
plate  be  put  into  a  stereoscope  and  identical  figures 


142  BINOCULAR  VISION. 

combined,  the  combination  is  absolute  and  the  plane  of 
the  combined  images  is  perfectly  flat ;  but  if  the  notes 
be  not  from  the  same  plate,  but  copied,  slight  variations 
are  unavoidable,  and  such  variations  will  show  them- 
selves in  a  gently  wavy  surface. 

Different  Forms  of  Perspective,— In  order  to  bring 
out  in  stronger  relief  the  distinctive  character  of  binoc- 
ular perspective,  it  is  necessary  to  mention  briefly  the 
several  different  forms  of  perspective.  There  are  many 
ways  in  which  we  judge  of  the  relative  distance  of  ob- 
jects in  the  field  of  view,  all  of  which  may  be  called 
modes  of  perspective. 

1.  Aerial  Perspective. — The  atmosphere  is  neither 
perfectly  transparent  nor  perfectly  colorless.     More  and 
more  distant  objects,  being  seen  through  greater  and 
greater  depths  of  this  medium,  become  therefore  dim- 
mer and  dimmer  and  bluer  and  bluer.     We  judge  of 
distance  in  this  way  ;  and  if  the  air  be  more  than  usually 
clear  or  more  than  usually  obscure,  we  may  misjudge, 

2.  Mathematical    Perspective.  —  Objects    become 
smaller  and  smaller  in  appearance,  and  nearer  and  near- 
er together,  the  farther  away  they  are.     Thus  streets  ap- 
pear narrower  and  narrower,  and  the  houses  lower  and 
lower,  with  distance.     Parallel  lines  of  all  kinds,  such 
as  railway  stringers,  bridge  timbers,  etc.,  converge  more 
and  more  to  a  vanishing  point. 

3.  Monocular  or  Focal  Perspective. — Objects  at  the 
distance  of  the  point  of  sight  are  distinct,  the  lenses 
being  focally  adjusted  for  that  distance ;  but  all  objects 
beyond  or  within  this  distance  are  dim.     ISTow,  we  are 
aware  of  a  greater  or  less  effort  of  adjustment  to  make 
a  distinct  image,  according  to  the  nearness  or  the  dis- 
tance of  the  object  looked  at.     This  is  also  a  means  of 
judging  of  the  distance  especially  of  near  objects. 


BINOCULAR  PERSPECTIVE.  143 

These  three  forms  may  all  be  called  monocular  ;  for 
they  would  equally  exist,  and  we  could  judge  of  dis- 
tance, so  far  as  these  modes  are  concerned,  equally  well, 
if  we  had  but  one  eye.  But  there  is  still  another,  viz. : 

4.  Binocular  Perspective. — In  order  to  combine  the 
images  of  objects  near  at  hand,  we  converge  the  optic 
axes  strongly ;  for  more  distant  objects,  less  and  less 
according  to  their  distance.  By  this  constant  change 
of  axial  adjustment  necessary  for  single  vision,  the  point 
of  optic  convergence  is  run  rapidly  back  and  forth  ;  and 
thus,  by  a  kind  of  rapid  and  almost  unconscious  trian- 
gulation,  we  estimate  the  relative  distance  of  objects  in 
the  field  of  view.  The  man  with  only  one  eye  can  not 
judge  by  this  method,  and  thus  often  misjudges  the 
distance  of  near  objects.  In  rapidly  dipping  a  pen  into 
an  inkstand,  or  putting  a  stopper  into  a  decanter,  the 
one-eyed  man  can  not  judge  so  accurately  as  the  two- 
eyed  man.  If  we  shut  one  eye  and  attempt  to  plunge 
the  finger  rapidly  into  the  open  mouth  of  a  bottle,  we 
are  very  apt  to  overreach  or  fall  short. 

As  clearness  of  vision  is  confined  to  a  small  area 
about  the  point  of  sight,  and  rapidly  fades  away  with 
increasing  distance  in  any  direction  on  the  same  plane, 
so  clearness  and  singleness  of  vision  are  confined  to  the 
distance  of  the  point  of  sight,  and  images  become  dim 
and  double  in  passing  beyond  or  to  this  side  of  that 
point.  Again,  as  we  sweep  the  point  of  sight  about 
laterally  over  a  wide  field  of  view,  and  gather  up  all 
the  distinct  impressions  into  one  mental  image,  so  we 
run  the  point  of  optic  convergence  back  and  forth,  and 
gather  up  a  mental  picture  of  the  relative  distance  of 
objects,  in  a  deep  field. 

These  different  forms  of  perspective  operate  for  very 
different  distances.  The  focal  adjustment  becomes  im- 


144  BINOCULAR  VISION. 

perceptible  for  distances  greater  than  about  20  feet. 
Judgments  based  on  this,  therefore,  are  limited  within 
that  distance.  Binocular  perspective  operates  percep- 
tibly for  much  greater  distance,  perhaps  several  hundred 
yards ;  but  beyond  this  it  becomes  imperceptible.  The 
other  two  forms,  the  mathematical  and  aerial,  operate 
without  limit. 

Now  the  painter  can  imitate  the  aerial  perspective. 
He  skillfully  diminishes  the  brightness,  dulls  the  sharp- 
ness of  outline,  and  blues  the  tinge  of  all  objects,  in 
proportion  to  their  supposed  distance,  so  as  to  produce 
the  effect  of  depth  of  air.  He  can  also  and  still  more 
perfectly  imitate  the  mathematical  perspective,  by  di- 
minishing the  size  of  objects  and  the  distance  between 
them  as  he  passes  from  his  foreground  to  his  back- 
ground. But  he  can  not  imitate  the  focal  perspective, 
and  still  less  can  he  imitate  the  binocular  perspective. 
This  is  artificially  given  only  in  the  stereoscope,  and  is 
the  glory  of  this  little  instrument.  Focal  perspective 
is  unimportant  to  the  painter,  because  imperceptible  at 
the  distance  at  which  pictures  are  usually  viewed ;  but 
the  want  of  binocular  perspective  in  paintings  interferes 
seriously  with  the  completeness  of  the  illusion.  There- 
fore the  illusion  is  more  complete  and  the  perspective 
comes  out  more  distinctly  when  we  look  with  only  one 
eye.  In  a  natural  scene  it  is  exactly  the  opposite  :  the 
perspective  is  far  more  perfect  with  both  eyes  open, 
because  then  all  the  forms  cooperate. 


CHAPTER  IY. 

THEORIES   OF  BINOCULAR   PERSPECTIVE. 

Wheatstone's  Theory. — To  Wheatstone  is  due  the 
credit  of  having  discovered  the  fact  that  two  slightly 
dissimilar  pictures — dissimilar  in  the  same  way  as  the 
two  retinal  images  of  a  solid  object  or  of  a  scene — when 
united,  produce  a  visual  effect  similar  to  that  produced 
by  an  actual  solid  object  or  an  actual  scene.  He  also 
invented  the  stereoscope  to  facilitate  the  combination 
of  such  pictures.  His  theory  of  these  effects  was  as 
follows  :  In  viewing  a  solid  object  or  a  scene,  two 
slightly  dissimilar  images  are  formed  in  the  two  eyes, 
as  already  explained ;  but  the  mind  completely  unites 
or  fuses  them  into  one.  Whenever  there  occurs  such 
complete  mental  fusion  of  images  really  dissimilar  in 
this  particular  way,  and  therefore  incapable  of  mathe- 
matical coincidence,  the  result  is  a  perception  of  depth 
of  space,  or  solidity,  or  relief.  In  the  stereoscope,  there- 
fore, he  supposes  that  the  two  slightly  dissimilar  pictures 
are  mentally  fused  into  one,  and  hence  the  appearance 
of  depth  of  space  follows  as  the  necessary  result  of  this 
mental  fusion. 

This  theory  is  still  widely  held  by  even  the  most 
recent  and  best  physiologists;  but  it  is  evidently  the 
result  of  imperfect  analysis  of  visual  impressions.  In 
stereoscopic  diagrams  it  is  always  possible  to  detect  the 


BINOCULAR  VISION. 

doubling  on  which  the  perception  of  depth  of  space  is 
based.  It  is  a  little  more  difficult  in  ordinary  stereo- 
scopic pictures,  and  in  natural  scenes ;  but  practice  and 
close  observation  will  always  detect  it  in  these  also.  It 
is  most  difficult  of  all  to  detect  it  in  the  case  of  single 
solid  objects /  but  this  is  mainly  because  the  doubling 
of  the  edges  of  such  objects  is  usually  out  of  the  line 
of  sight.  Even  where  we  can  not  detect  the  doubling, 
and  yet  binocularly  perceive  depth  of  space,  such  per- 
ception must  be  regarded  as  an  example  of  unconscious 
cerebration.  We  actually  ground  our  judgments  upon  im- 
pressions which  do  not  emerge  into  clear  consciousness. 

Observe  the  degrees  of  this  unconsciousness.  Even 
the  doubling  of  the  forefinger,  when  held  up  before  the 
eyes  while  we  gaze  at  the  wall,  is  undetected  by  some 
persons.  To  such  the  binocular  perspective  here  seems 
to  be  a  simple  primary  sense-per.ception.  But  the 
slightest  scientific  observation  is  sufficient  to  separate 
this  apparently  simple  impression  into  its  component 
elements,  and  thus  to  show  that  it  is  a  judgment  based 
on  simpler  elements.  Next,  the  doubling  of  objects  in 
the  foreground  of  a  scene  or  stereoscopic  picture,  when 
the  background  is  regarded,  fails  to  appear  in  conscious- 
ness. But  analysis  again  shows  that  the  perception  of 
depth  here  also  is  not  simple,  but  decomposable  into 
simpler  elements.  Close  observation  again  detects  the 
elements  on  which  judgment  is  based.  Therefore, 
where  we  can  not  detect  the  simpler  elements,  we 
must  believe  that  they  still  exist  and  that  judgments 
are  based  upon  them.  Nothing  can  be  more  certain 
than  that  complete  fusion  never  takes  place ;  and  if  it 
seems  so  to  us.  it  is  only  because  we  do  not  observe 
and  analyze  with  sufficient  care. 

Wheatstone's  theory  therefore  seems  true  only  to 


THEORIES   OF  BINOCULAR  PERSPECTIVE.  14.7 

the  unpracticed  and  unobservant.  It  makes  that  simple 
and  primary  which  is  capable  of  analysis  into  simpler 
elements.  It  is  therefore  a  popular,  not  a  scientific 
theory.  It  cuts,  but  does  not  loose,  the  Gordian  knot. 

Briicke's  Theory. — Briicke  and  Brewster  and  Prevost, 
by  more  refined  observation  and  more  careful  analysis, 
easily  perceived  that  there  was  in  reality  no  mental 
fusion  of  two  dissimilar  images.  Their  view,  most 
completely  expressed  by  Briicke,*  is  that  which  has 
been  assumed  in  the  foregoing  account  and  explanation 
of  binocular  phenomena.  It  is,  that  in  regarding  a 
solid  object  or  a  natural  scene,  or  two  stereoscopic  pic- 
tures in  a  stereoscope,  the  eyes  are  in  incessant  uncon- 
scious motion,  and  the  observer,  by  alternately  greater 
and  less  convergence  of  the  axes,  combines  successively 
the  different  parts  of  the  two  pictures  as  seen  by  the 
two  eyes,  and  thus  by  running  the  point  of  sight  back 
and  forth  reaches  by  trial  a  distinct  perception  of  bin- 
ocular perspective  or  binocular  relief,  or  depth  of  space 
between  foreground  and  background. 

That  double  images  are  really  necessary  to  binocular 
perspective,  as  maintained  by  Briicke,  is  abundantly 
proved  by  the  experiments  already  given  on  that  sub- 
ject. But  one  additional  experiment  may  be  given 
here  to  complete  the  proof. 

Experiment. — As  I  look  out  of  my  window,  I  see 
the  clothes-lines  of  a  neighboring  family,  about  40  feet 
distant.  Two  of  these  are  parallel,  but  one  about  5  or 
6  feet  beyond  the  other.  The  lines  being  horizontal, 
no  double  images  are  visible  when  the  head  is  erect. 
In  this  position  I  am  unable  to  tell  which  line  is  the 
farther  off.  But  when  I  turn  the  head  to  one  side,  so 
that  the  interocular  line  is  at  right  angles  to  the  cords, 

*  "Archives  des  Scisnces,"  tome  iii,  p.  142  (1858). 


14:8  BINOCULAR  VISION. 

immediately  their  relative  distance  comes  out  with  great 
distinctness. 

This  theory  is  a  great  advance  on  the  preceding. 
It  is  really  a  scientific  theory,  since  it  is  based  on  an 
analysis  of  our  visual  judgments.  It  is  also  in  part  a 
true  theory,  and  for  this  reason,  in  anticipation  of  what 
we  believe  to  be  a  more  perfect  theory,  we  have  used 
it  in  the  explanation  of  many  visual  phenomena  in  the 
preceding  pages.  But  it  is  evidently  not  the  whole 
truth,  as  we  now  proceed  to  show. 

1.  If  we  place  one  object  before  another  in  the 
median  plane  of  sight,  even  when  we  look  steadily  and 
without  change  of  optic  convergence  at  the  one  or  the 
other,  we  distinctly  perceive  the  depth  of  space  between 
them.     Evidently  no  trial  combination,  no  running  of 
the  point  of  sight  back  and  forth,  and  successive  union 
and  disunion  of  the  images,  are  necessary  for  the  per- 
ception of  binocular  relief.    But  if  it  be  said  that  change 
of  optic  convergence  does  indeed  take  place,  only  rapidly 
and  unconsciously,  I  proceed  to  prove  that  such  is  not 
the  case. 

2.  Dove's  Experiment.  —  The  instantaneous  percep- 
tion of  binocular  relief  is  demonstrated  by  the  now  cele- 
brated experiment  of  Dove.     If  a  natural  object,  or  a 
scene,  or  two  stereoscopic  pictures,  be  viewed  by  the 
light  of  an  electric  spark  or  a  succession  of  electric 
sparks,   the   perspective   is  perfect,  even   though   the 
duration  of  such  a  spark  is  only  -g-j-^-g-  of  a  second  of 
time.     On  a  dark  night  the  relative  distance  of  objects 
is  perfectly  perceived  by  the  light  of  a  flash  of  light- 
ning, wrhich  according  to  Arago  lasts  only  -j-oW?*  and 
according  to  Rood  -^-J^f  °f  a  second.     It  is  inconceiva- 


*  Arago,  "  CEuvrcs  Completes,"  tome  iv,  p.  70. 

f  Rood,  "American  Journal  of  Science  and  Arts,"  vol.  i,  1870,  p.  15. 


THEORIES  OF  BINOCULAR  PERSPECTIVE.  149 

ble  that  there  should  be  any  change  of  optic  conver- 
gence, any  running  of  the  point  of  sight  back  and  forth, 
in  the  space  of  ^-¥^oir  Part  °^  a  second-  Evidently, 
therefore,  binocular  perspective  may  be  perceived  with- 
out such  change  of  convergence.  This  point  is  certainly 
one  of  capital  importance.  The  instantaneous  percep- 
tion of  relief  is  fatal  to  Briicke's  theory  in  its  pure  un- 
modified form.  I  have  therefore  repeated  Dove's  ex- 
periment with  care,  varying  it  in  every  possibly  way, 
so  as  to  guard  against  every  source  of  error.  These 
experiments  completely  confirm  Dove's  result,  and  es- 
tablish beyond  doubt  the  instantaneous  perception  of 
binocular  relief.  From  a  large  number  of  experiments 
I  select  a  few  of  the  most  conclusive  and  most  easily 
repeated.  The  spark  apparatus  used  was  a  Ritchie's 
Ruhmkorff  capable  of  producing  sparks  12  inches  long. 
A  Leyden  jar  was  introduced  into  the  circuit  to  increase 
the  brilliancy  of  the  sparks. 

Experiment  1. — I  select  stereoscopic  pictures  in 
which  other  forms  of  perspective  are  wanting,  or  near- 
ly so  ;  skeleton  geometric  diagrams  are  the  best.  Stand- 
ing in  a  perfectly  dark  room,  and  viewing  these  in  a 
stereoscope  by  the  light  of  a  succession  of  sparks,  the 
perspective  is  perfectly  distinct  with  two  eyes,  but  not 
at  all  with  one  eye. 

Experiment  2. — I  select  a  stereoscopic  card  like  the 
last,  except  that  mathematical  perspective  is  also  strong 
— such,  for  example,  as  a  view  of  the  interior  of  a 
bridgeway.  Of  course,  as  in  the  last  case,  the  natural 
perspective  is  instantly  perceived  in  the  stereoscope; 
but  this  might  be  attributed  to  the  mathematical  per- 
spective. But  now  hold  the  card  in  the  hand  and  unite 
the  pictures  with  the  naked  eyes  by  squinting :  the  in- 
verse perspective  described  on  page  135  will  be  brought 


150  BINOCULAR   VISION.   • 

out  with  perfect  clearness  with  two  eyes,  but  the  nat- 
ural perspective  (mathematical)  returns  when  we  shut 
one  eye.  This  experiment  is  conclusive,  being  removed 
from  even  the  suspicion  of  the  effect  being  the  result 
of  other  forms  of  perspective ;  for  in  this  case  the  bin- 
ocular is  opposed  to  all  other  forms  of  perspective,  over- 
bears them,  and  reverses  the  perspective. 

So  much  for  combination  of  stereoscopic  pictures, 
whether  beyond  the  plane  of  the  card,  as  in  the  stereo- 
scope, or  on  this  side  the  plane  of  the  card,  as  in  naked- 
eye  combination  by  squinting.  We  will  next  try  the 
viewing  of  natural  objects,  eliminating  as  before  as 
much  as  possible  other  forms  of  perspective. 

Experiment  3. — Let  two  objects,  as  two  brass  balls, 
of  the  same  size,  be  hung  by  invisible  threads,  one  about 
5  or  6  feet  distant,  and  the  other  about  1  foot  farther. 
At  this  distance  focal  adjustment  is  practically  the  same 
for  the  two  balls,  and  thus  this  mode  of  judging  of  rel- 
ative distance  is  eliminated.  Let  the  balls  be  placed  in 
the  median  plane  of  sight,  or  nearly  so,  in  such  wise 
that  their  relative  distance  may  be  easily  detected  with 
two  eyes,  but  not  with  one.  In  the  latter  case — i.  e., 
with  one  eye — they  look  like  two  balls  side  by  side,  the 
one  a  trifle  larger  than  the  other.  Now,  after  darken- 
ing the  room,  try  the  experiment  by  the  instantaneous 
flash  of  electric  sparks.  It  will  be  found  that  under 
these  conditions  also  the  relative  distance  is  perceived 
with  perfect  clearness  with  two  eyes,  but  not  with  one. 

It  is  certain,  then,  that  binocular  perspective  is  per- 
ceived instantly,  and  therefore  without  the  trial  com- 
binations of  different  parts  of  the  two  images,  as  main- 
tained by^griicke,  Brewster,  and  others. 

two  rival  theories,  therefore,  the  case 
r^hkatstone  is  right  in  so  far  as  he  asserts 


B- 


THEOEIES  OF   BINOCULAR  PERSPECTIVE. 

immediate  or  instantaneous  perception  of  relief,  but 
wrong  in  supposing  that  there  is  a  complete  mental  fu- 
sion of  the  two  images.  Briicke  is  right  in  asserting 
that  binocular  perspective  is  a  judgment  based  on  the 
perception  of  double  images,  but  wrong  in  supposing 
change  of  optic  convergence  and  successive  trial  com- 
binations of  different  parts  of  the  two  images  to  be  a 
necessary  part  of  the  evidence  on  which  judgment  is 
based. 

My  own  View  is  an  attempt  to  bring  together  and 
reconcile  what  is  true  in  both  of  the  preceding  views. 
This,  which  I  conceive  to  be  the  only  true  and  complete 
theory,  is  hinted  at,  but  not  distinctly  formulated,  by 
Helmholtz.*  I  have  strongly  insisted  upon  it  in  all 
my  papers  on  this  subject.  I  quote  from  one  of  them  :  f 
"  All  objects  or  points  of  objects,  either  beyond  or 
nearer  than  the  point  of  sight,  are  doubled,  but  differ- 
ently— the  former  homonymously,  the  latter  heterony- 
mously.  The  double  images  in  the  former  case  are 
united  \)j  less  convergence,  in  the  latter  case  by  greater 
convergence,  of  the  optic  axes.  Now,  the  observer 
knows  instinctively  and  without  trial,  in  any  case  of 
double  images,  whether  they  will  be  united  by  greater 
or  less  optic  convergence,  and  therefore  never  makes  a 
mistake,  or  attempts  to  unite  by  making  a  wrong  move- 
ment of  the  optic  axes.  In  other  words,  the  eye  (or  the 
mind)  instinctively  distinguishes  homonymous  from 
heteronymous  images,  referring  the  former  to  objects 
beyond,  and  the  latter  to  objects  this  side  of,  the  point 
of  sight"  Or  again :  In  case  of  double  images,  "  each 
eye,  as  it  were,  knows  its  own  image,"  although  such 
knowledge  does  not  emerge  into  distinct  consciousness. 


'  "  Optique  Physiologique,"  p.  939 
f  "American  Journal  of  Science  and  Arts,"  vol.  ii,  1871,  p.  425. 


152  BINOCULAR  VISION. 

Tims,  then,  I  conclude  that  the  mind  perceives  re- 
lief instantly,  but  not  immediately ;  for  it  does  so  by 
means  of.  double  images,  as  just  explained.  This  is  all 
that  is  absolutely  necessary  for  the  perception  of  relief ; 
but  it  is  probable — nay,  it  is  certain — that  the  relief  is 
made  clearer  by  a  ranging  of  the  point  of  sight  back 
and  forth,  and  a  successive  combination  of  the  different 
parts  of  the  object  or  scene  or  pictures,  as  maintained 
by  Briicke. 

Return  to  the  Comparison  of  the  Eye  and  the  Camera. 
— It  is  time  now  to  return  to,  and  to  continue,  our  com- 
parison of  the  eye  and  the  photographic  camera.  We 
have  seen  that  both  the  camera  and  the  eye  are  equally 
optical  instruments  contrived  for  the  purpose  of  making 
an  image';  but  we  have  also  seen  that  in  both  this  image 
is  only  a  means  by  which  to  attain  a  higher  end,  viz., 
to  make  a  photographic  picture  in  the  one  case,  and  to 
accomplish  distinct  vision  in  the  other.  In  both  also, 
in  order  to  accomplish  its  higher  purpose,  there  must 
be  a  sensitive  receiving  plate,  viz.,  the  iodized  silver 
plate  in  the  one,  and  the  living  retina  in  the  other.  In 
both,  finally,  there  are  wonderful  changes,  chemical  or 
molecular,  or  both,  in  the  sensitive  plate.  Let  us  then 
continue  the  comparison. 

1.  In  the  photographic  camera  when  accomplishing 
its  work  there  are  three  images  which  may  be  mentally 
separated  and  described.  First,  the  light-image.  This 
is  what  we  see  on  the  ground-glass  plate.  It  comes  and 
goes  with  the  object  in  front.  It  is  the  facsimile  in 
form  and  color  of  the  object,  but  diminished  in  size 
and  inverted  in  position.  Second,  the  invisible  image. 
When  the  ground-glass  plate  is  withdrawn  and  the 
sensitive  plate  substituted,  the  light-image  falling  on 
this  plate  determines  in  it  wonderful  molecular  changes, 


THEORIES  OF  BINOCULAR  PERSPECTIVE.  153 

which  are  graduated  in  intensity  exactly  according  to 
the  intensity  and  kind  of  light  in  the  light-image :  the 
aggregate  effect  is  therefore  rightly  called  an  image, 
though  it  is  invisible.  Third,  the  visible  image,  or 
picture.  The  operator  then  takes  the  plate  with  the 
invisible  image  to  a  dark  room,  and  applies  certain 
chemicals  which  develop  the  image — i.  e.,  which  de- 
termine certain  permanent  chemical  changes,  which  in 
intensity  and  kind  are  exactly  proportioned  to  the  an- 
tecedent molecular  changes,  and  therefore  graduated 
over  the  surface  exactly  as  the  molecular  changes  of 
the  invisible  image  were  graduated,  and  hence  also 
exactly  as  the  light  of  the  light-image  was  graduated. 
This  is  the  permanent  photographic  picture — the  fac- 
simile in  form  of  the  object  which  produced  it. 

So  also  in  the  work  of  the  eye,  vision,  we  may  men- 
tally separate  and  may  describe  three  corresponding 
images.  First,  there  is  the  light-image,  which  is  formed 
in  the  dead  as  well  as  the  living  eye.  Second,  the  in- 
visible image.  The  light-image,  falling  on  the  sensitive 
living  retina,  determines  in  its  substance  molecular 
changes  which  are  graduated  in  intensity  and  kind  ex- 
actly as  the  light  of  the  light-image  is  graduated  in  in- 
tensity and  color,  and  may  therefore  be  rightly  called 
an  image,  even  though  it  be  invisible,  and  the  nature 
of  the  molecular  changes  be  inscrutable.  Third,  the 
external  visible  image.  The  invisible  image,  or  the 
molecular  changes  which  constitute  it,  is  transmitted 
to  the  brain,  and  by  the  brain  or  the  mind  is  projected 
outward  into  space,  and  hangs  there  as  a  visible  exter- 
nal image,  the  sign  and  facsimile  in  form  and  color  of 
the  object  which  produced  it. 

2.  Again,  as  there  are  certain  effects  which  can  not 
be  produced  by  one  camera — as  two  cameras  from  two 


154  BINOCULAR  VISION. 

positions  take  two  slightly  different  pictures  of  the  same 
object  or  the  same  scene,  which  when  combined  in  the 
stereoscope  produce  the  clear  perception  of  depth  of 
space — even  so  the  two  eyes  act  as  a  double  camera  in 
taking  and  a  stereoscope  in  combining  two  slightly  dif- 
ferent images  of  every  object  or  scene,  so  as  to  give  a 
clear  perception  of  binocular  perspective. 

We  have  thus  carried  the  comparison  as  far  as  com- 
parison is  possible.  But  there  is,  this  essential  differ- 
ence between  the  two — essential  because  found  every- 
where between  human  and  natural  mechanism :  In  the 
one  case  we  trace  mechanism  and  physics  and  chemistry 
throughout.  In  the  other  we  also  trace  mechanism, 
exquisite  mechanism,  but  only  to  a  certain  point,  be- 
yond which  we  discover  something  higher  than  mere 
mechanism.  We  trace  physics  and  chemistry  to  a  cer- 
tain point,  but  as  we  pursue  the  investigation  we  find 
something  superphysical  and  superchemical,  or  else  a 
physics  and  a  chemistry  far  higher  than  any  we  yet 
know.  At  a  certain  point  molecular  and  chemical 
change  is  replaced  by  sensation,  perception,  judgment, 
thought,  emotion.  We  pass  suddenly  into  another  and 
wholly  different  world,  where  reigns  an  entirely  differ- 
ent order  of  phenomena.  The  connection  between 
these  two  orders  of  phenomena,  the  material  and  the 
mental,  although  it  is  right  here  in  the  phenomena  of 
the  senses,  and  although  we  bring  to  bear  upon  it  the 
microscopic  eye  of  science,  is  absolutely  incomprehen- 
sible, and  must  in  the  very  nature  of  things  always 
remain  so.  Certain  vibrations  of  the  molecules  of  the 
brain,  certain  oxidations,  with  the  formation  of  carbonic 
acid,  water,  and  urea,  on  the  one  side,  and  there  appear 
on  the  other  sensations,  consciousness,  thoughts,  desires, 
volitions.  There  are,  as  it  were,  two  sheets  of  blotting 


THEORIES   OF  BINOCULAR  PERSPECTIVE.  155 

paper  pasted  together ;  the  one  is  the  brain,  the  other 
is  the  mind.  Certain  ink-scratches  and  ink-blotchings, 
utterly  meaningless,  on  the  one,  soak  through  and  ap- 
pear on  the  other  as  intelligible  writing.  But  how 
or  why  we  know  not,  and  can  never  hope  even  to 
guess. 


CHAPTER  Y. 

JUDGMENT  OF  DISTANCE,  SIZE,  AND   FORM. 

WE  are  now  prepared  to  understand  the  modes  of 
estimating  distance,  size,  and  form ;  for  these  modes 
are  founded  partly  on  monocular  and  partly  on  binoc- 
ular vision. 

As  already  stated,  the  direct  and  simple  sense-im- 
pressions given  by  the  optic  nerve  are  light,  its  inten- 
sity, its  color,  and  its  direction.  These  can  not  be 
analyzed  into  simpler  elements,  but  distance,  size,  and 
form  are  judgments  based  upon  these. 

Distance. — We  judge  of  distance  by  means  of  the 
different  forms  of  perspective  already  described  on 
page  142:  1.  By  focal  adjustment,  or  monocular  per- 
spective. The  eye  adjusts  itself  for  distinct  vision  for 
all  distances  from  infinite  distance  to  five  inches.  By 
experience  we  know  distance  from  the  amount  of  effort 
necessary  to  adjust  for  perfect  image,  and  therefore 
distinct  vision.  Judgments  based  on  this  are  tolerably 
accurate  from  5  inches  to  several  yards.  Beyond  20 
feet  it  is  too  small  to  be  appreciable.  2.  By  axial 
adjustment,  or  binocular  perspective.  The  greater  or 
less  amount  of  optic  convergence  necessary  to  produce 
single  vision  is  a  far  more  accurate  mode  of  judging  of 
distance  than  the  last.  It  is  reliable  from  near  the  root 


JUDGMENT   OF  DISTANCE,  SIZE,  AND  FORM.          157 

of  the  nose  to  the  distance  of  two  or  three  hundred 
yards.  Beyond  this  it  also  becomes  inappreciable,  for 
the  doubling  of  objects  is  only  equal  to  the  interocular 
distance.  3.  By  mathematical  perspective.  By  dimi- 
nution of  the  apparent  size  of  known  objects  and  the 
convergence  of  parallel  lines  we  judge  of  distance  with 
great  accuracy  and  almost  without  limit.  4.  By  aerial 
perspective.  Change  of  color  and  brightness  of  all  ob- 
jects, in  proportion  to  the  depth  of  air  looked  through, 
is  still  another  mode  of  judging  of  distance,  which, 
though  far  less  accurate  than  the  last,  like  it  extends 
without  limit.  Estimates  of  distance,  being  judgments, 
are  liable  to  error.  Such  errors  are  often  called  decep- 
tions of  sense,  but  they  are  not  so.  They  are  errors  of 
judgment  based  upon  true  deliverances  of  sense. 

Size. — The  size  of  an  unknown  object  is  judged  by 
its  angular  diameter,  or  the  size  of  its  retinal  image 

FIG.  54. 


multiplied  by  its  estimated  distance.  For  example,  an 
image  a,  Fig.  54,  occupies  a  certain  space  on  the  retina. 
Now,  evidently,  precisely  the  same  image  would  be 
made  by  a  small  object  at  A,  or  a  proportionally  larger 
similar  object  at  A',  or  a  still  larger  similar  one  at  A". 
Therefore  the  estimated  size  of  the  object  which  pro- 
duced the  image  will  depend  upon  the  distance  we 
imagine  the  object  to  be  from  us,  this  distance  being  of 
course  estimated  by  the  different  forms  of  perspective 


158  BINOCULAR  VISION. 

given  above.  Thus,  estimates  of  size  and  distance  are 
very  closely  related  to  each  other,  and  an  error  in  the 
one  will  involve  an  error  in  the  other.  If  we  misjudge 
the  distance  of  an  unknown  object,  we  will  to  the  same 
degree  and  in  the  same  direction  misjudge  its  size :  if 
our  estimate  of  distance  be  too  great,  our  judgment  of 
size  will  also  and  to  the  same  extent  be  too  great ;  if 
our  estimate  of  distance  be  too  small,  so  also  will  be  our 
judgment  of  size.  Contrarily,  if  we  make  a  mistake  as 
to  the  size  of  a  known  object — as,  for  example,  if  we 
mistake  a  boy  for  a  man — we  will  also  to  the  same  ex- 
tent misjudge  the  distance. 

Yery  many  illustrations  may  be  given  of  this  gen- 
eral principle,  but  by  far  the  most  perfect  are  the  ex- 
periments on  combination  of  the  regular  figures  given 
on  pages  114  and  115.  In  combining  by  squinting,  in 
proportion  as  the  point  of  optic  convergence,  and  there- 
fore the  imagined  place  of  the  pattern,  becomes  nearer 
and  nearer,  the  figures  of  the  pattern  become  smaller. 
On  the  other  hand,  when  we  combine  beyond  the  plane 
of  the  pattern,  so  that  the  more  distant  point  of  optic 
convergence  makes  the  imagined  place  of  the  pattern 
farther  off  than  its  real  place,  then  the  figures  are  magni- 
fied in  the  same  proportion.  So  also  stereoscopic  scenes 
are  larger  or  smaller  than  the  actual  picture,  according 
as  we  combine  beyond  or  on  this  side  the  plane  of  the 
picture. 

Illustrations  like  the  above  are  most  conclusive, 
because  the  relation  of  size  and  distance  is  seen  to  be 
mathematically  proportioned ;  but  many  familiar  illus- 
trations may  be  given. 

1.  While  intently  regarding  the  paper  on  which  I 
am  writing,  or  the  page  which  I  am  reading,  a  fly  or 
gnat  passes  across  the  extreme  margin  of  the  field  of 


JUDGMENT   OF  DISTANCE,  SIZE,  AND  FORM.          159 

view  toward  the  open  window.  I  mistake  it  for  a  large 
bird  like  a  hawk  flying  ait  some  distance  in  the  open 
air.  The  reason  is,  that  under  these  conditions  we  have 
no  means  of  judging  either  of  form  or  of  distance  ;  the 
size  and  distance  of  an  object  are  therefore  left  wholly  to 
the  suggestions  of  the  imagination.  If  we  look  around 
so  as  to  see  the  form  distinctly,  and  to  bring  binocular 
or  other  forms  of  perspective  to  bear  on  the  subject, 
we  quickly  detect  our  error  and  correct  our  judgment. 

2.  Where  there  are  no  means  of  judging  of  distance, 
we  can  not  estimate  size,  and  different  persons  will 
estimate  differently.     Thus,  the  sun  or  moon  seems  to 
some  persons  the  size  of  a  saucer,  to  some  that  of  a 
dinner-plate,  and  to  some  that  of  the  head  of  a  barrel. 
But  under  peculiar  conditions  we  imagine  them  much 
larger.     For  example,  a  pine-tree  stands  on  the  western 
horizon  about  a  mile  distant.    I  am  accustomed  to  judge 
of  the  size  and  distance  of  trees.     This  one  seems  to  me 
at  least  20  feet  across  the  branches.     The  evening  sun 
slowly  descends  and  sets  behind  the  tree.     It  fills  and 
much  more  than  fills  its  branches.     Again,  here  in 
Berkeley,  on  a  clear  day,  the  Farallone  Islands,  40  miles 
distant,  are  distinctly  seen  through  the  Golden  Gate. 
I  think  no  one  would  say  that  the  larger  one  seems  less 
than  100  feet  across.     At  certain  seasons  in  spring  and 
autumn  the  sun  sets  behind  the  Farallones,  and  these 
islands  are  projected  in  clear  outline  as  black  spots  on 
his  disk. 

3.  Illustrations  meet  us  on  every  side.     In  fog,  ob- 
jects look  larger,  because,  through  excess  of  aerial  per- 
spective, we  overestimate  distance.  •  On  the  high  Sierra, 
or  the  Colorado  mountains,  or  anywhere  on  the  high 
interior  plateau,  the  clearness  of  the  air  and  consequent 
distinctness  of  distant  objects  are  such,  that  we  imagine 


160  BINOCULAR  VISION. 

objects  to  be  nearer  and  therefore  smaller  than  they 
really  are. 

Form. — Outline  form  is  a  combination  of  directions 
of  component  radiants.  In  a  ring  of  stars,  the  direction 
of  each  star  is  given  immediately ;  the  combination  of 
these  several  directions  gives  the  ring.  This  is  so  sim- 
ple and  immediate  a  judgment,  that  it  may  almost  be 
called  a  direct  sense-perception.  It  is  apparently  a  di- 
rect perception  of  the  form  of  the  retinal  image.  It  is 
so  sure  and  immediate  that  it  is  not  liable  to  error ;  yet 
it  is  capable  of  analysis  into  simpler  elements,  as  shown 
above. 

Solid  form  is  a  far  more  complex  judgment,  and 
therefore  liable  to  error.  We  judge  of  solid  form 
partly  by  binocular  perspective  and  partly  by  shades 
of  light.  The  roundness  of  a  column  is  perceived  part- 
ly by  the  greater  optic  convergence  necessary  to  see  dis- 
tinctly the  nearer  central  parts  than  the  farther  marginal 
parts,  and  partly  by  the  shading  of  light  on  the  different 
parts.  The  latter  effect  can  be  perfectly  imitated  by 
the  painter,  but  not  the  former.  Hence  the  illusion 
produced  by  the  painter  is  most  perfect  at  a  distance 
where  binocular  perspective  is  very  small,  but  is  de- 
stroyed by  near  approach.  Hence  also  the  roundness 
of  a  painted  column  is  most  perfect  when  looking  with 
one  eye,  but  of  a  natural  column  when  looking  with 
two  eyes. 

Gradation  of  Judgments. — Intensity,  color,  and  di- 
rection of  light  are  simple  impressions  which  can  not 
be  further  analyzed.  Next  come  outline  form  and 
surface  contents,  which  may  indeed  be  analyzed  into 
combination  of  directions,  but  yet  the  perception  is  so 
direct  and  so  certain  that  it  may  well  be  called  imme- 
diate. Next  conies  solid  form,  which,  as  we  have  seen, 


JUDGMENT   OF  DISTANCE,  SIZE,  AND   FORM. 

is  a  more  complex  judgment  based  on  simple  elements, 
and  therefore  may  be  deceived.  Next  come  the  closely 
related  and  still  more  complex  judgments  of  size  and 
distance,  which  are  therefore  still  more  liable  to  error. 
These  latter  judgments  become  more  and  more  com- 
plex as  the  objects  in  the  field  of  view  become  more 
numerous  and  more  complex  in  form  and  varied  in 
position ;  as,  for  example,  the  judgments  of  form,  size, 
and  distance  of  all  the  objects  in  an  extended  natural 
scene.  All  these  seem  to  the  uninstructed  as  immedi- 
ate instinctive  perceptions,  and  mistakes  are  supposed 
to  be  the  result  of  deceptions  of  sense  instead  of  errors 
of  judgment,  as  they  really  are.  Judgments  like  these, 
which  are  so  quickly  made  that  the  process  has  largely 
dropped  out  of  consciousness,  I  shall  call  visual  judg- 
ments. But  these  higher  and  more  complex  visual 
judgments  pass,  by  almost  insensible  degrees,  into  still 
higher  and  more  complex  intellectual  judgments.  Thus 
from  simple  sense-impressions  we  pass  without  break 
through  the  various  grades  of  visual  judgments  to  the 
lower  intellectual  judgments,  and  from  these  again 
through  various  grades  of  complexity  to  the  highest 
efforts  of  the  cultured  mind. 

ISrow,  as  visual  judgments  seem  to  the  uninstructed 
primary,  immediate,  and  simple  perceptions,  so  also 
among  intellectual  judgments  many  seem  to  those  unin- 
structed in  psychology  and  unskilled  in  mental  analysis 
as  primary,  immediate,  instinctive,  or  innate,  and  there- 
fore certain.  But,  as  the  study  of  visual  phenomena 
teaches  that  these  visual  judgments  are  capable  of  an- 
alysis into  simpler  elements,  and  therefore  liable  to 
error,  so  also  the  study  of  psychology  should  teach  us 
that  many  of  the  so-called  instinctive  judgments,  pri- 
mary intuitions,  etc.,  may  also  be  capable  of  analysis, 


162  BINOCULAR  VISION. 

and  therefore  liable  to  error.  Further,  it  is  evident 
that  the  so-called  facts  of  consciousness,  in  the  one  field 
as  in  the  other,  can  not  be  considered  reliable  until  sub- 
jected to  rigid  analysis.  The  study  of  visual  (especially 
binocular  visual)  phenomena  is  peculiarly  valuable  :  first, 
in  teaching  us  that  so  called  immediate  intuitions  are  in 
many  cases  only  judgments,  the  processes  of  which  have 
dropped  out  of  consciousness ;  and,  second,  in  teaching 
us  the  habit  of  analysis  of  such  apparently  simple  in- 
tuitions. 


RETROSPECT. 

We  have  now  given  in  clear  outline  the  most  im- 
portant phenomena  of  vision  and  their  explanation.  It 
will  not  be  amiss,  before  proceeding  further,  to  look 
back  over  what  we  have  passed,  and  justify  its  logical 
order. 

There  are  three  essentially  different  modes  of  re- 
garding the  eye,  which  must  be  combined  in  a  complete 
account  of  this  organ.  We  have  taken  up  these  suc- 
cessively. First,  we  treated  of  the  eye  as  an  optical 
instrument  contrived  to  form  a  perfect  image,  every 
focal  point  of  which  shall  correspond  with  a  radiant 
point  in  the  object.  This  is  a  purely  physical  inves- 
tigation. Second,  we  treated  of  the  structure  of  the 
retina,  especially  its  bacillary  layer,  and  showed  how 
from  this  structure  resulted  the  wonderful  property  of 
corresponding  points  retinal  and  spatial,  and  the  ex- 
change between  these  by  impression  and  perceptive 
projection,  and  how  the  law  of  direction  and  all  the 
phenomena  of  monocular  vision  flow  out  of  this  prop- 
erty. Third,  we  treated  of  the  still  more  wonderful 


RETROSPECT.  163 

correspondence  of  the  two  retince  point  for  point,  and 
therefore  of  their  spatial  representatives  point  for  point ; 
and  considered  how  by  ocular  motion  the  two  images  of 
the  same  object  are  made  to  fall  on  corresponding  points 
of  the  two  retinae,  and  their  spatial  representatives  are 
thereby  made  to  coincide  and  become  one ;  and  how, 
finally,  all  the  phenomena  of  binocular  vision  flow  from 
this  property. 

We  have  therefore  apparently  covered  the  ground 
originally  laid  out.  But  there  are  still  a  number  of 
questions  on  binocular  vision,  somewhat  more  abstruse 
and  more  disputed  than  the  preceding,  but  of  so  high 
interest  that  they  must  not  be  wholly  neglected.  The 
remaining  chapters  will  be  devoted  to  these. 


:    3 


PAET   III. 

ON    SOME    DISPUTED    POINTS    IN 
BINOCULAR    VISION. 


CHAPTER  I. 

LAWS   OF  OCULAR  MOTION. 
SECTION  I.—  LAWS  OF  PARALLEL  MOTION.—  LISTING'S  LAW. 


have  already  (page  69)  spoken  of  spectral  im- 
ages produced  by  strong  impressions  on  the  retina.  It 
is  evident  that  these,  being  the  result  of  impressions 
branded  upon  the  retina  and  remaining  there  for  some 
time,  must  while  they  remain  follow  all  the  motions  of 
the  eye  with  the  greatest  exactness.  They  are  specially 
adapted,  therefore,  for  detecting  motions  of  the  eyes, 
such  as  slight  torsions  or  rotations  on  the  optic  axes, 
which  could  not  be  detected  in  any  other  way. 

Experiment  1.  —  Let  the  experimental  room  be  dark- 
ened by  closing  the  shutters,  but  allow  light  to  enter 
through  a  vertical  slit  between  the  shutters  of  one  win- 
dow. Standing  before  the  window  with  head  erect, 
gaze  steadily  at  the  slit  until  a  strong  impression  is 
branded  in  upon  the  vertical  meridian  of  the  retina. 
If  we  now  turn  about  to  the  blank  wall,  we  see  a  very 


LAWS   OF  PARALLEL   MOTION.  165 

distinct  colored  vertical  spectral  image  of  tlie  slit. 
Placing  now  the  eyes  in  the  primary  position — i.  e., 
with  face  perpendicular  and  eyes  looking  horizontally 
— if,  without  changing  the  position  of  the  head,  we 
turn  the  eyes  to  the  right  or  left  horizontally,  the  im- 
age remains  vertical.  Also  if  we  turn  the  eyes  upward 
or  downward  by  elevating  or  depressing  the  visual  plane, 
the  image  remains  vertical.  But  if,  with  the  visual 
plane  elevated  extremely,  say  40°,  we  cause  the  eyes  to 
travel  to  the  right  or  left,  say  also  40°,  or  if  we  turn 
the  eyes  from  their  original  primary  position  obliquely 
upward  and  to  one  side  to  the  same  point,  the  image 
is  no  longer  vertical,  but  leans  decidedly  to  the  same 
side ;  i.  e.,  in  going  to  the  right,  the  image  leans  to  the 

right,  thus —  /  ;   in  going  to  the  left,  it  leans  to  the 

left,  thus — \  .  If,  on  the  contrary,  the  visual  plane 
be  depressed,  then  motion  of  the  eyes  to  the  right  causes 
the  image  to  lean  to  the  left,  thus —  V  ;  while  motion 

to  the  left  causes  it  to  lean  to  the  right,  thus —   / . 

Experiment  2. — If,  instead  of  a  vertical,  we  use  a 
horizontal  slit  in  the  window,  and  thus  obtain  a  hori- 
zontal image  and  throw  it  on  the  wall  as  before,  then, 
if  the  image  has  been  made  with  the  eyes  in  the  pri- 
mary position,  it  will  be  seen  on  the  wall  perfectly 
horizontal.  Furthermore,  if  the  eyes  travel  right  and 
left  in  the  primary  visual  plane,  or  upward  and  down- 
ward by  elevating  or  depressing  the  visual  plane,  the 
image  retains  its  perfect  horizontality.  But  if,  with 
the  visual  plane  elevated,  we  cause  .the  point  of  sight 


166  DISPUTED  POINTS   IN   BINOCULAR   VISION. 

to  travel  to  the  one  side  or  the  other,  the  image  is  seen 
to  turn  to  the  opposite  side;  i.  e.,  when  the  eyes  turn 
to  the  right,  the  image  turns  to  the  left,  thus — ^^*" ; 
when  they  turn  to  the  left,  the  image  rotates  to  the 
right,  thus — ^^-^ .  If  the  visual  plane  be  depressed, 
then  motion  to  the  right  causes  the  image  to  rotate  to 
the  right  (x\x),  and  motion  to  the  left  causes  it  to 
rotate  to  the  left  (^^^). 

These  rotations  of  the  image  depend  wholly  on  the 
oblique  position  of  the  eyes,  and  it  makes  no  difference 
how  that  oblique  position  is  reached — whether  by  mo- 
tion along  rectangular  coordinates,  as  in  the  experiments, 
or  by  oblique  motion  from  the  primary  position.  Fur- 
thermore, the  amount  of  rotation  of  the  image  increases 
with  the  amount  of  elevation  or  depression  of  the  visual 
plane,  and  the  amount  of  lateral  motion  of  the  eyes. 

Experiment  3. — The  fact  of  rotation  or  torsion  of 
the  images,  and  the  direction  of  that  torsion,  are  easily 
determined  by  the  somewhat  rough  methods  detailed 
above ;  but  if  we  desire  to  measure  the  amount  of  tor- 
sion,  the  wall  or  other  experimental  plane  must  be 
covered  with  rectangular  coordinates,  vertical  and  hori- 
zontal. By  experimenting  in  this  way,  I  find  that  for 
extreme  oblique  positions  the  torsion  of  the  vertical 
image  on  the  vertical  lines  of  the  experimental  plane 
is  about  15°,  but  the  torsion  of  the  horizontal  image  on 
the  horizontal  lines  is  only  about  5°.  The  reason  of 
this  difference  will  be  explained  farther  on. 

Putting  now  all  these  results  together,  the  fol- 
lowing diagram  (Fig.  55)  gives  the  position  of  the 
vertical  and  horizontal  images  when  projected  on  a 
vertical  plane  for  all  positions  of  the  point  of  sight. 
Simple  inspection  of  the  diagram  is  sufficient  to  show 


LAWS   OF   PARALLEL   MOTION.  167 

that  the  inclination  or  torsion  of  the  vertical  image  on 
the  true  verticals,  and  that  of  the  horizontal  image  on  the 
true  horizontals,  are  in  opposite  directions.  If  torsion 


FIG.  55. 


DlAJBAM  SHOWING  THE  INCLINATION  OF  VERTICAL  AND  HORIZONTAL  IMAGES  FOB 
ALL  POSITIONS  OF  THE  POINT  OF  SIGHT. 

of  the  images  show  torsion  of  the  eye,  there  must  be  a 
fallacy  somewhere.  The  one  or  the  other  must  be 
wrong ;  for  when  one  indicates  torsion  to  the  right,  the 
other  indicates  torsion  to  the  left,  and  vice  versa.  To 
show  this  contradictory  testimony  more  clearly,  and  thus 
to  prove  that  there  is  a  fallacy  here,  we  make  another 
experiment. 

Experiment  4- — Make  a  rectangular  cross-slit  in  the 
window,  gaze  steadily  upon  it  until  the  spectral  impres- 


168  DISPUTED  POINTS  IN  BINOCULAR  VISIOX. 

sion  is  made  on  the  retina,  and  then  cast  the  image  on  the 
wall.  In  the  primary  position  of  the  eyes  it  is  of  course 
a  perfect  rectangular  cross.  Now  turn  the  eyes  to  the 
extreme  upper  right-hand  corner  of  the  wall.  The  cross, 
by  opposite  rotations  of  the  two  parts,  is  seen  distorted 

thus -r~^ .    Looking  upward  and  to  the  left,  it  is 

\ 

seen  thus—  ""V*-*  Oblique  motion  downward  and  to 
the  right  makes  it  appear  thus —  ^W ,  and  to  the  left 


thus ^.     It  will  be  observed  that  this  is  exactly  the 

manner  in  which  the  lines  cross  in  the  diagram,  and  we 
have  placed  crosses  in  the  corners  to  indicate  that  fact. 

Evidently  the  cause  of  the  contradictory  evidence 
of  the  two  images  is  projection  on  a  plane  inclined  at 
various  angles  to  the  line  of  sight.  The  diagram  is  a 
correct  representation  of  the  phenomena  as  seen  pro- 
jected on  a  vertical  plane,  but  is  not  a  correct  represen- 
tation of  the  torsions  of  the  eyes.  To  eliminate  this 
source  of  fallacy  and  get  the  true  torsion  of  the  eyes, 
we  must  project  the  cross-image  on  a  plane  in  every 
case  perpendicular  to  the  line  of  sight. 

Experiment  5. — Prepare  an  experimental  plane  a 
yard  square,  make  a  rectangular  cross  in  the  center,  and 
set  up  a  perfectly  perpendicular  rod  at  the  point  of 
crossing.  Fix  the  plane  in  a  position  inclined  30°  to 
40°  with  the  vertical,  and  obliquely  to  the  right  side 
and  above,  so  that,  when  sitting  before  the  experimen- 
tal window  and  turning  the  eyes  extremely  upward  and 


LAWS  OF  PARALLEL  MOTION.  169 

to  the  right,  the  observer  looks  directly  on  the  top  of 
the  rod,  and  this  latter  is  projected  against  the  plane  as 
a  round  spot.  We  thus  know  that  the  line  of  sight  is 
perpendicular  to  the  plane.  Now,  after  gazing  at  the 
cross-slit  in  the  window  until  the  spectral  impression  is 
made  on  the  retina,  without  moving  the  head,  cast  the 
image  on  the  center  of  the  plane  by  turning  the  eyes 
obliquely  upward  and  to  the  right.  The  rectangular 
cross-image  rotates,  loth  parts  alike,  so  as  to  retain  per- 
fectly its  rectangular  symmetry,  to  the  right,  thus  — 

">-  ,  showing  unmistakably  a  torsion  of  the  eyes  in  the 
same  direction.  If  the  plane  be  arranged  similarly  on 
the  left  side,  the  cross  turns  to  the  left,  thus  — 


the  plane  be  arranged  below  and  to  the  right,  so  that 
the  eyes  turned  obliquely  downward  and  to  the  right 
shall  look  perpendicularly  upon  it,  the  cross  will  turn 


to  the  left,  thus  —  -\  •     ^  similarly  arranged  on  the 


left  side,  the  cross  will  turn  to  the  right,  thus  — 

In  all  cases  the  rectangular  symmetry  is  perfectly  pre- 
served, a  sure  sign  that  there  is  no  error  by  projection, 
and  that  they  truly  represent  the  torsion  of  the  eyes. 

Experiment  6.  —  In  order  to  neglect  no  means  of 
testing  the  truth  of  this  conclusion,  we  will  make  one 
more  experiment,  using  the  sky  as  the  plane  upon 
which  to  project  the  image.  This  spatial  concave  is  of 
course  everywhere  at  right  angles  to  the  line  of  sight, 
and  therefore  is  free  from  any  suspicion  of  error  from 
projection.  Standing  in  the  open  air  before  a  vertical 


170  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

flag-staff,  I  gaze  upon  it  steadily  until  its  image  is,  as  it 
were,  burned  into  the  vertical  meridian  of  the  retina. 
Now,  without  moving  the  head,  I  turn  the  eyes  ob- 
liquely upward  and  to  the  right,  and  the  image  leans 
decidedly  to  the  right ;  and  turning  to  the  left,  the  image 
leans  to  the  left.  In  this  position  of  the  head,  of  course, 
the  ground  prevents  us  from  making  the  same  experi- 
ment with  the  visual  plane  depressed.  I  therefore 
vary  the  experiment  slightly.  Sitting  directly  in 
front  of  the  college  building,  with  the  morning  sun 
shining  obliquely  on  its  face,  the  light-colored  perpen- 
dicular pilasters  gleam  in  the  sunshine,  and  contrast 
strongly  with  the  shadows  which  border  their  northern 
margin.  Gazing  steadily  at  the  building,  I  easily  get  a 
strong  spectral  image  of  the  whole  structure,  with  its 
vertical  and  its  horizontal  lines.  Now  throwing  myself 
flat  on  my  back,  I  see  the  image  perfectly  erect  on  the 
zenith.  Turning  the  eyes  upward  toward  the  brows 
and  to  the  right  and  left,  then  downward  toward  the 
feet  and  to  the  right  and  left,  the  whole  image  of  the 
building  rotates  precisely  as  indicated  in  my  previous 
experiments. 

Evidently,  then,  in  the  diagram  Fig.  55,  the  verticals 
give  true  results,  but  the  horizontals  deceptive  results 
by  projection.  Why  this  is  so  is  easily  explained.  Sup- 
pose an  observer  to  stand  in  a  room  before  a  vertical 
wall ;  suppose  him  further  to  be  surrounded  by  a  spher- 
ical wire  cage  constructed  of  rectangular  spherical  co- 
ordinates, or  meridians  and  parallels,  with  the  eye  in 
the  center  and  the  pole  in  the  zenith.  Evidently,  the 
surface  of  this  spherical  concave  is  everywhere  perpen- 
dicular to  the  line  of  sight,  and  therefore,  like  the  sky, 
is  the  proper  surface  of  projection.  Evidently,  also,  the 
meridians  and  parallels  everywhsre  at  right  angles  to 


LAWS  OF  PARALLEL  MOTION. 


171 


each  other  are  the  true  coordinates  wherewith  to  com- 
pare the  images,  vertical  and  horizontal,  in  order  to 
determine  the  direction  and  amount  of  their  rotation. 
Now  the  simple  question  is,  "  How  do  these  true  rec- 
tangular coordinates  project  themselves  on  the  wall  to 
an  eye  placed  in  the  center,  or  how  would  their  shad- 


FIG.  56. 


DIAGRAM  SHOWING  THE  PROJECTION  OF  A  SYSTEM  OF  SPHERICAL  COSRDINATES  ON 
A  VERTICAL  PLANE. 

ows  be  cast  by  a  light  in  the  center  ? "  It  is  evident 
that  the  meridians  would  project  as  straight  verticals, 
but  the  parallels  not  as  straight  lines,  but  as  hyperbolic 
curves,  increasing  in  curvature  as  we  go  upward  or 
downward.  The  diagram  Fig.  56  shows  how  the 


172          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

spherical  coordinates  would  project  on  a  vertical  wall. 
By  calculation  or  by  careful  plotting  it  may  be  shown 
that  at  an  angle  of  elevation  or  depression  of  40°,  and 
a  lateral  angle  of  the  same  amount,  the  inclination  of 
the  hyperbolic  curve  on  the  horizontals  of  the  wall  will 
be  about  20°.  Now  a  rectangular  cross-image,  if  un- 
rotated,  would  project  as  the  crosses  in  the  corners ;  i.  e., 
the  vertical  arm  would  project  vertically,  but  the  hori- 
zontal arm  would  be  inclined  20°  with  the  horizontal, 
so  that  the  angles  of  the  cross  would  be  about  70°  and 
110°.  Now  rotate  these  crosses  15°,  the 
right  upper  one  to  the  right,  the  left  up- 
per one  to  the  left,  the  right  lowrer  to  the 
left,  and  the  left  lower  to  the  right,  and 
we  have  the  precise  phenomena  repre- 
sented by  the  diagram  Fig.  55 ;  i.  e.,  the 
verticals  are  turned  15°  right  or  left  as 
the  case  may  be,  and  the  horizontals  in 
the  opposite  direction,  but  only  5°.  Fig. 
57  illustrates  this  in  the  case  of  the  right-hand  upper 
cross-image — the  heavy  cross  representing  the  cross  un- 
rotated,  and  the  lighter  one  the  same  rotated  15°  to  the 
right  by  extreme  obliquity  of  the  line  of  sight. 

Therefore,  the  diagram  which  truly  represents  the 
torsion  of  the  eye  in  various  positions,  or  the  torsion  of 
the  cross-image  when  referred  to  a  spherical  concave 
perpendicular  to  the  line  of  sight  in  every  position,  is 
represented  in  Fig.  58.  Simple  inspection  of  this  fig- 
ure shows  the  real  direction  and  amount  of  rotation 
both  of  the  vertical  and  the  horizontal  image  for  every 
position  of  the  line  of  sight.  The  crosses  in  the  cor- 
ners show  that  there  is  no  distortion  by  projection. 

We  are  justified  therefore  in  formulating  the  laws 
of  parallel  motion  of  the  eyes  thus : 


LAWS  OF  PARALLEL   MOTION.  173 

1.  When  the  eyes  move  together  in  the  primary  plane 
to  the  one  side  or  the  other,  or  in  a  vertical  plane  up 
or  down,  there  is  no  rotation  on  the  optic  axes,  or  tor- 
sion.. 

FIG.  58. 


DIAGRAM  SHOWING  THE  TRUE  TORSION  OF  TOE  EYE  FOR  VARIOUS  POSITIONS  OF 
THE  POIMT  OF  SIGHT. 

2.  When  the  visual  plane  is  elevated  and  the  eyes 
move  to  the  right,  they  rotate  to  the  right  /  when  they 
move  to  the  left,  they  rotate  to  the  left. 

3.  When  the  visual  plane  is  depressed,  motion  of 
the  eyes  to  the  right  is  accompanied  with  rotation  to  the 
left,  and  motion  to  the  left  with  rotation  to  the  right. 

4.  These  laws  may  be  all  generalized  into  one,  viz. : 
When  the  vertical  and  lateral  angles  have  the  same 


174:          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

sign*  the  rotation  is  positive  (to  the  right)  •  when  they 
have  contrary  signs,  the  rotation  is  negative  (to  the  left). 

The  law  now  announced  as  the  result  of  experiment 
is  evidently  identical  with  the  law  of  Listing,  which 
has  been  formulated  by  Listing  himself  thus : 

"  When  the  line  of  sight  passes  from  the  primary 
position  to  any  other  position,  the  angle  of  torsion  of 
the  eye  in  its  second  position  is  the  same  as  if  the  eye 
had  come  to  this  second  position  by  turning  about  a 
fixed  axis  perpendicular  both  to  the  first  and  the  second 
position  of  the  line  of  sight"  f 

Now  an  axis  which  satisfies  these  conditions  can  be 
none  other  than  an  equatorial  axis,  or  at  least  an  axis 
in  a  plane  perpendicular  to  the  polar  axis.  In  turning 
from  side  to  side  in  the  primary  plane,  it  is  a  vertical 
equatorial  axis.  In  turning  up  and  down  vertically, 
it  is  a  horizontal  equatorial  axis.  In  turning  obliquely, 
as  in  the  experiments  on  torsion,  it  is  an  oblique  equa- 
torial axis.  Now  take  a  globe,  and,  placing  the  equator 
in  a  vertical  plane,  make  a  distinct  vertical  and  hori- 
zontal mark  across  the  pole.  Then  turn  the  globe  on 
an  oblique  equatorial  axis,  so  that  the  pole  shall  look 
upward  and  to  the  right.  It  will  be  seen  that  the  polar 
cross  is  no  longer  vertical  and  horizontal,  but  is  rotated 
to  the  right.  If  the  globe  be  turned  upward  and  to  the 
left,  the  polar  cross  will  rotate  to  the  left ;  if  downward 
and  to  the  right,  it  will  rotate  to  the  left ;  and  if  to  the 
left,  it  will  rotate  to  the  right.  In  a  word,  the  rotation 
in  every  case  is  the  same  as  given  in  the  above  laws 
determined  by  experiment. 

*  In  reference  to  a  vertical  line,  positions  to  the  right  are  positive 
and  to  the  left  negative ;  in  reference  to  a  horizontal  line,  above  is  posi- 
tive and  below  negative. 

f  Helmholtz,  "  Optiquc  Physiologique,"  p.  606. 


LAWS  OF  PARALLEL  MOTION.  175 

Contrary  Statement  by  Helmholtz. — We  have  given 
these  laws  and  their  experimental  proof  in  some  detail, 
and  have  taken  some  pains  to  show  that  they  are  in 
complete  accord  with  Listing's  law,  because  Helmholtz 
in  his  great  work  on  "  Physiological  Optics  "  has  given 
these  laws  of  ocular  motion  the  very  reverse  of  mine. 
I  quote  from  the  French  edition  of  1867,  which  is  not 
only  the  latest  but  also  the  most  authoritative  edition 
of  the  work : 

"  When  the  plane  of  sight  is  directed  upward,  lateral 
displacements  to  the  right  make  the  eye  turn  to  the  left, 
and  displacements  to  the  left  make  it  turn  to  the  right. 

"  When  the  plane  of  sight  is  depressed,  lateral  dis- 
placements to  the  right  are  accompanied  with  torsion 
to  the  right,  and  vice  versa. 

"  In  other  words,  when  the  vertical  and  lateral  an- 
gles are  both  of  the  same  sign,  the  torsion  is  negative  / 
when  they  are  of  contrary  signs,  the  torsion  is  posi- 
tive." * 

We  have  demonstrated  the  very  reverse  of  every 
one  of  these  propositions,  and  we  have  also  shown  that 
they  are  inconsistent  with  Listing's  law  as  quoted  by 
Helmholtz  himself.  The  experiments  by  which  Helm- 
holtz seeks  to  determine  the  torsions  of  the  eye  are  the 
same  as  those  already  described  under  experiments  1  and 
2,  page  165.  The  results  which  he  reaches  are  also  the 
same  as  those  reached  by  myself,  except  that  he  makes 
the  inclination  of  the  vertical  image  on  the  verticals  of 
the  wall,  and  of  the  horizontal  image  on  the  horizontals 
of  the  wall,  equal  to  each  other,  while  I  make  the  in- 
clination of  the  verticals  much  greater.  The  diagram  by 
which  he  embodies  all  these  results  is  also  similar  to  my 
diagram,  Fig.  55,  except  that  in  his  the  horizontal  and 

*  "  Optique  Physiologique,"  p.  602. 


1T6 


DISPUTED  POINTS  IN  BINOCULAR  VISION. 


vertical  curves  are  exactly  similar,  while  in  mine  the 
curves  of  the  verticals  are  much  greater.  He  also,  like 
myself,  admits  that  there  is  a  fallacy  by  projection. 
But  unaccountably  he  imagines  that  the  inclination  of 
the  horizontal  image  on  the  true  horizontal  gives  true 
results,  and  the  inclination  of  the  vertical  image  on  the 
true  vertical  deceptive  results  by  projection ;  therefore 
he  imagines-  the  eye  to  turn  exactly  the  reverse  of  the 
reality.  Experiments  5  and  6,  under  conditions  elim- 
inating errors  by  projection,  prove  the  falseness  of  his 
results.  The  reader  who  desires  to  follow  up  this  sub- 
ject will  find  it  discussed  in  an  article  by  the  writer  re- 
ferred to  below.* 

The  Rotation  only  Apparent. — There  can  be  no  doubt, 
then,  that  when  the  eye  passes  from  its  primary  position 
to  an  oblique  position,  the  vertical  meridian  of  the  ret- 
ina is  no  longer  vertical,  but  inclined.  If  we  observed 

the  iris  of  another  per- 
son, we  should  see  that 
it  had  turned  as  a  wheel. 
In  deference  to  the 
usage  of  other  writers 
and  to  the  appearance, 
I  have  spoken  of  this  as 
a  rotation  on  the  optic 
axis,  but  it  is  so  in  ap- 
pearance only,  and  not 
in  reality;  for  the  mo- 
tion of  the  eye,  being 
always  on  an  axis  in  a 
plane  perpendicular  to  the  polar  or  optic  axis,  can  not 
be  resolved  into  a  rotation  about  that  axis.  A  simple 
experiment  will  show  the  kind  of  rotation  which  takes 

*  "American  Journal  of  Science  and  Arts,"  III,  vol.  xx,  1880,  p.  83. 


LAWS  OF  CONVERGENT  MOTION.  177 

place  in  bringing  the  eye  to  an  oblique  position.  Take 
a  circular  card,  Fig.  59,  and  make  on  it  a  rectangular 
cross  which  shall  represent  the  vertical  (V  V)  and  hori- 
zontal (H  H)  meridians  of  the  retina.  A  small  central 
circle  p  represents  the  pupil.  Now  take  hold  of  the 
disk  with  the  thumb  and  finger  of  the  right  hand  at 
the  points  V  V,  and  place  this  line  in  a  vertical  plane. 
Then  tip  the  disk  up  so  that  the  pupil  p  shall  look  up- 
ward 45°  or  more,  but  the  line  V  V  still  remaining  in 
the  vertical  plane.  Finally,  with  the  finger  of  the  left 
hand  turn  the  disk  on  the  axis  V  Vto  the  left.  It  will  be 
seen  that  V  Fis  no  longer  vertical,  norJIII  horizontal ; 
but  some  other  line  x  x  is  vertical,  and  y  y  horizontal. 
In  other  words,  the  whole  disk  seems  to  have  rotated 
to  the  left.  But  this  is  evidently  no  true  rotation  on  a 
polar  axis,  but  only  an  apparent  rotation  consequent 
upon  reference  to  a  new  vertical  meridian  of  space.  It 
does  not  take  place  in  the  primary  plane,  because  there 
all  the  spatial  meridians  are  parallel,  but  only  in  an 
elevated  or  depressed  plane,  because  the  spatial  merid- 
ians are  there  convergent.  I  shall  therefore  hereafter 
call  this  apparent  rotation  on  the  optic  axis  torsion. 
This  is  the  more  important,  because  there  is  a  real  ro- 
tation on  the  optic  axis,  which  we  shall  speak  of  under 
the  next  head. 


SECTION  II.— LAWS  OF  CONVERGENT  MOTION. 

We  have  thus  far  confined  ourselves  to  explanation 
of  the  laws  which  govern  the  eyes  when  they  move  in 
the  same  direction  with  axes  parallel,  as  in  looking  from 
side  to  side  or  up  and  down.  I  have  called  this  the  law 
of  parallel  motion.  We  now  come  to  speak  of  the  laws 


178          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

which  govern  the  eyes  when  they  move  in  opposite  di- 
rections, as  in  convergence.  These  I  will  call  the  laws 
of  convergent  motion. 

In  convergence  there  is  not  merely  an  apparent 
rotation  or  torsion,  but  a  real  rotation  of  the  eyes  on 
the  optic  axes ;  and  since  the  motions  are  in  opposite 
directions,  the  rotations  are  also  opposite.  But,  except 
in  very  strong  convergence,  the  rotation  is  small  and 
difficult  to  observe,  and  therefore  has  been  either  over- 
looked or  denied  by  many  observers.  As  the  existence 
or  non-existence  of  this  rotation  has  an  important  bear- 
ing on  the  much-vexed  question  of  the  horopter,  it  is 
important  that  proof  should  be  accumulated  even  to 
demonstration. 

The  first  difficulty  which  meets  us  in  experimenting 
on  this  subject  is,  that  spectral  images,  which  are  such 
delicate  indicators  of  ocular  motion,  are  almost  useless 
here.  In  parallel  motion  of  the  eyes  these  images  fol- 
low every  movement  with  the  utmost  exactness,  but  in 
convergent  motion  they  do  not.  Suppose,  for  example, 
with  the  eyes  parallel  or  nearly  so,  a  spectral  image  is 
branded  on  the  vertical  meridians  of  both  eyes.  In 
convergence  each  eye  may  move  through  45°  or  more, 
but  the  place  of  the  spectral  image  is  the  game,  viz., 
directly  in  front.  The  eye  also  in  extreme  conver- 
gence may  rotate  on  the  optic  axis  10°,  but  the  vertical 
image  remains  still  perfectly  vertical.  The  reason  of 
this  is,  that  the  two  retinal  images  are  on  corresponding- 
points,  and  therefore  by  the  law  of  corresponding  points 
their  external  representatives  are  indissolubly  united. 
In  moving  the  eyes  in  opposite  directions,  it  is  impos- 
sible that  the  images  should  move  except  by  separating ; 
but  separation,  either  complete  or  partial,  is  impossible 
without  violating  the  law  of  corresponding  points — a 


LAWS  OF  CONVERGENT  MOTION.  179 

law  which  is  never  violated  under  any  circumstances 
whatsoever.  Actual  objects  therefore,  not  spectral  im- 
ages, must  be  used  in  these  experiments. 

As  the  experiments  about  to  be  described  are  among 
the  most  difficult  in  the  whole  field  of  binocular  vision, 
and  as  in  many  of  them  it  is  absolutely  necessary  that 
the  primary  visual  plane  should  be  perfectly  horizontal, 
I  must  first  define  what  we  mean  by  the  primary  visual 
plane,  and  show  how  it  may  be  made  perfectly  hori- 
zontal. 

Take  a  thin  plate,  like  a  cardboard ;  place  its  edge 
on  the  root  of  the  nose  and  the  card  at  right  angles  to 
the  line  of  the  face,  in  such  wise  that  the  plane  of  the 
card  shall  cut  through  the  center  of  the  two  pupils,  and 
you  can  see  only  its  edge.  The  card  is  then  in  the 
primary  visual  plane.  Keeping  the  position  of  the  card 
fixed  in  relation  to  the  face,  the  face  may  be  elevated 
or  depressed,  and  the  card  will  be  also  elevated  or  de- 
pressed, but  will  remain  in  the  primary  visual  plane. 
But  if  the  card  be  elevated  or  depressed  so  as  to  make 
a  different  angle  with  the  line  of  the  face,  then  the  vis- 
ual plane  is  elevated  or  depressed  above  or  below  the 
primary  position.  When  the  head  is  erect  and  the  line 
of  the  face  vertical,  the  primary  visual  plane  is  hori- 
zontal. Suppose  we  wish  now  to  look  at  a  vertical  wall 
in  such  wise  that  the  primary  visual  plane  shall  be  per- 
fectly horizontal.  We  first 
mark  on  the  wall  a  horizon-  FlG- co- 

tal  line  exactly  the  height        **( 
of  the  root   of    the   nose.  \ 

Standing  then  say  6   feet 

off,  and  shutting  first  one  eye  and  then  the  other,  we 
bring  the  image  of  the  lowest  part  of  the  root  of  the 
nose  directly  across  the  line.  The  primary  plane  is 


180 


DISPUTED  POINTS  IN  BINOCULAR  VISION. 


then  perfectly  horizontal.  In  Fig.  60,  n  and  n'  are  the 
curves  of  the  outline  of  the  root  of  the  nose  as  seen  by 
the  right  and  left  eye  respectively,  and  n  n'  is  the  hori- 
zontal line  on  the  wall.  We  are  now  prepared  to  make 
our  experiments. 

Experiment  1. — Prepare  a  plane  2  feet  long  and  1 
foot  wide.  Dividing  this  by  a  middle  line  into  two 
equal  squares,  let  one  of  the  halves  be  painted  black 
and  the  other  white.  Let  the  whole  be  covered  with 
rectangular  coordinates,  vertical  and  horizontal,  on  the 
black  half  the  lines  being  white  and  on  the  white  half 

FIG.  61. 


black,  as  in  Fig.  61.  Near  the  middle  of  the  two  square 
halves,  and  at  the  crossing  of  a  vertical  and  horizontal 
line,  make  two  small  circles,  c  cf.  Set  up  this  plane  on 
the  table  in  a  perfectly  vertical  position,  and  at  a  dis- 
tance of  2  or  3  feet.  Rest  the  chin  on  the  table  im- 
mediately in  front  of  the  plane,  with  a  book  or  other 
support  under  the  chin,  so  that  the  root  of  the  nose 
shall  be  exactly  the  same  height  as  the  circles,  wThich  in 
this  case  is  about  6  inches.  Now,  shutting  alternately 


LAWS  OF  CONVERGENT  MOTION.  181 

one  eye  and  the  other,  bring  the  image  of  the  lowest 
part  of  the  root  of  the  nose  coincident  with  the  hori- 
zontal line  running  through  the  circles.  The  primary 
plane  is  now  perfectly  horizontal,  and  therefore  at  right 
angles  to  the  experimental  plane.  Now,  finally,  con- 
verge the  eyes  until  the  right  eye  looks  directly  at  the 
left  circle,  and  the  left  eye  at  the  right  circle,  and  of 
course  the  two  circles  combine.  If  one  is  practiced  in 
such  experiments,  and  observes  closely,  he  will  see  that 
the  vertical  lines  of  the  two  squares  (which  can  be 
readily  distinguished,  because  those  of  the  one  are  white 
and  of  the  other  black),  as  they  approach  and  pass  over 
one  another  successively,  are  not  perfectly  parallel, 

r\ll 

but  make  a  small  angle,  thus—    U  ;  and  ako  that  the 

angle  increases  as  the  convergence  is  pushed  farther 
and  farther,  so  that  lines  even  beyond  the  circles  are 
brought  successively  together.  Similarly  also  the  hori- 
zontals cut  each  other  at  a  small  angle,  but  this  fact  is 
not  so  easy  to  observe  as  in  the  case  of  the  verticals. 

Such  are  the  phenomena ;  now  for  the  interpretation. 
Tt  must  be  remembered  that  images  of  objects  differ 
wholly  from  spectral  images  in  this,  viz. :  that  spectral 
images,  being  fixed  impressions  on  the  retina,  follow 
the  motions  of  the  eye  with  perfect  exactness ;  while, 
images  of  objects  being  movable  on  the  retina,  their 
external  representatives  in  convergence  seem  to  move 
in  a  direction  contrary  to  the  motions  of  the  eye  (page 
107).  This  is  true  of  all  motions,  whether  by  transfer 
of  the  point  of  sight  or  by  rotation  about  the  optic 
axes.  Now,  in  the  above  experiment,  the  images  of 
the  two  squares  with  all  their  lines  seem  to  rotate  about 
the  point  of  sight  outward — i.  e.,  the  right-hand  square 
to  the  right,  and  the  left-hand  square  to  the  left.  At 


182 


DISPUTED   POINTS  IN  BINOCULAR  VISION. 


FIG.  62. 


first  sight  this  might  seem  to  indicate  a  contrary  rota- 
tion of  the  eyes,  viz.,  inward.  But  not  so  ;  for,  observe, 
the  field  of  view  of  the  right  eye  is  the  left  or  black 
square,  and  the  field  of  view  of  the  left  eye  is  the  right  or 

white  square.  The  right-eye 
field  turns  to  the  left,  showing 
a  rotation  of  the  right  eye  to 
the  right ;  while  the  left-eye 
field  turns  to  the  right,  show- 
ing a  rotation  of  the  left  eye 
to  the  left.  Thus  the  two 
eyes  in  convergence  rotate  out- 
ward. This  is  shown  in  the 
diagram  Fig.  62,  in  which 
c  cr  is  the  experimental  plane. 
The  arrows  show  the  direc- 
tion of  rotation  of  the  images 
of  the  plane  and  of  the  eyes. 
Experiment  2. — When  one  becomes  accustomed  to 
experiments  of  this  kind,  he  can  make  them  in  many 
ways.  I  find  the  following,  one  of  the  easiest  and  most 
convenient :  Measure  the  exact  height  of  the  root  of  the 
nose  upon  the  sash  of  the  open  window,  and  mark  it. 
Stand  with  head  erect  about  3  or  4  feet  from  the  win- 
dow. Using  the  cross-bars  of  the  sash-frame  as  hori- 
zontal lines,  arrange  the  head  so  that  the  two  images 
of  the  root  of  the  nose  shall  be  exactly  the  same  height 
as  the  mark.  The  primary  plane  is  now  horizontal. 
Now  converge  the  eyes  until  the  dark  outer  jambs  or 
sides  of  the  frame  of  the  sash  approach  each  other. 
This  will  be  very  distinct  on  account  of  the  bright  light 
between  them.  It  will  be  seen  that  the  frames  come 

r\ll 
together,  not  parallel,  but -as  a  sharp  V,  thus —  \  I  ,  r  and 


LAWS  OF  CONVERGENT   MOTION.  183 

I  being  the  right-  and  left-eye  images  respectively.  I 
find  that  when  I  stand  at  a  distance  from  the  window 
equal  to  the  width  of  the  sash,  the  angle  between  the 
two  jambs  as  they  come  together  is  about  15°,  showing 
a  rotation  of  each  eye  outward  7°  30'.  When  standing 
still  nearer,  so  that  the  convergence  is  extreme,  the 
angle  is  20°  or  more,  showing  a  rotation  of  each  eye  of 
10°  or  more. 

In  all  these  experiments  the  extremest  care  is  neces- 
sary to  insure  the  perfect  horizontally  of  the  visual 
plane.  The  slightest  upward  or  downward  looking 
vitiates  the  result  by  introducing  mathematical  perspec- 
tive. If  there  were  no  rotation,  then  looking  upward 
and  converging  would  bring  the  jambs  together  by 

perspective,  thus —  A  ;  looking  downward,  thus —  W  ; 

looking  horizontal,  parallel,  thus —  .  But  on  account 
of  rotation,  looking  horizontal  brings  them  together 

r\ll  ry      il 

thus —   y  ;  downward,  at  higher  angle,   thus —  W  • 

Looking  upward  more  and  more,  the  angle  decreases 
till  it  becomes  0  (i.  e.,  the  jambs  parallel),  and  then  in- 
verted. I  find  that  in  the  previous  experiment,  stand- 
ing from  the  window  the  distance  of  its  width,  I  must 
elevate  the  plane  of  vision  about  6° — i.  e.,  I  must  look 
about  8  or  9  inches  above  the  mark — to  make  the  jambs 
parallel.  This  is  therefore  a  good  method  of  measuring 
amount  of  rotation. 

Experiment  3. — A  far  more  accurate  mode  of  mea- 
suring the  amount  of  rotation  is  by  constructing  dia- 
grams on  a  plane  similar  to  the  one  used  in  experiment 
1,  but  in  which  the  verticals  and  horizontals  are  both 
inclined  on  the  true  verticals  and  true  horizontals  in  a 


184: 


DISPUTED   POINTS   IN  BINOCULAR  VISION. 


direction  contrary  to  the  rotation  of  the  eyes — i.  e.,  in- 
ward— and  then  determining  the  degree  of  convergence 
necessary  to  make  them  come  together  perfectly  par- 
allel. I  find  that  for  my  eyes,  when  the  verticals  are 
thus  inclined  in  each  square  1  J°  with  the  true  vertical, 
and  therefore  make  an  angle  of  2^°  with  each  other 
(Fig.  63),  they  come  together  parallel  when  the  point 
of  sight  is  7  inches  from  the  root  of  the  nose.  When 
the  angle  of  inclination  in  each  is  2£°  with  the  true 
vertical,  and  therefore  5°  with  each  other,  the  point  of 

FIG.  63. 


VERTICALS  AND  HORIZONTALS  INCLINED  \\°. 

sight  must  be  4  inches  off.  When  the  inclination  with 
the  true  vertical  is  5°,  and  therefore  10°  with  each 
other,  the  point  of  sight  is  2' 2  inches.  Finally,  when 
the  inclination  with  the  true  vertical  is  10°  or  20°  with 
each  other,  then  they  can  be  brought  together  parallel 
only  by  the  extremest  convergence,  the  point  of  sight 
being  then  only  a  quarter  of  an  inch  in  front  of  the 
root  of  the  nose.  In  the  diagram  Fig.  63  the  lines, 
both  vertical  and  horizontal,  are  inclined  inward  1J°, 
and  therefore  the  verticals  of  the  two  squares  make  an 


LAWS  OF  CONVERGENT   MOTION.  185 

angle  with  each  other  of  2^°.  It  is  therefore  a  reduced 
facsimile  of  the  plane  used.  The  coordinate  lines  coincide 
when  the  point  of  sight  is  7  inches  from  the  root  of  the 
nose. 

In  the  cases  of  extreme  convergence  mentioned 
above,  I  find  that  for  perfect  coincidence  of  both  ver- 
ticals and  horizontals  it  is  necessary  that  the  inclination 
of  the  verticals  with  the  true  vertical  must  be  greater 
than  that  of  the  horizontals  with  the  true  horizontal ;  so 
that  the  little  squares  are  not  perfect  squares.  Thus, when 

FIG.  64. 


VERTICALS  INCLINED  10",  HOKIZONTALS  6". 

the  verticals  incline  5°,  the  horizontals  must  incline  only 
3£° ;  when  the  verticals  incline  10°,  the  horizontals  in- 
cline only  5°.  Fig.  64  is  a  reduced  facsimile  of  this  last 
case  of  extreme  convergence.  I  can  not  account  for  this, 
except  by  a  distortion  of  the  ocular  globe  by  the  unu- 
sual and  unnatural  strain  on  the  muscles,  especially  the 
oblique  muscles  of  the  eyes.  It  may  be  that  other  eyes 
are  more  rigid  than  mine,  and  suffer  less  distortion. 

The  above  is  by  far  the  most  refined  method  of 
proving  rotation,  and  of  measuring  its  amount.     But 


186  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

so  difficult  are  these  experiments,  and  so  delusive  the 
phenomena,  that  it  is  necessary  to  prove  it  in  many 
ways.  Another  method  is  by  means  of  ocular  spectra. 
We  have  already  shown  that  these  are  not  so  well 
adapted  to  experiments  in  convergent  motion  as  they 
are  in  parallel  motion.  For  example,  two  brands  on 
the  vertical  meridians  of  the  two  retinae  produce  spec- 
tral images  which  are  perfectly  united  (p.  178).  Now 
in  strong  convergence,  when  the  two  eyes  rotate  out- 
ward, the  two  images  will  not  separate  or  cross  each 

\/r 
other,  thus  —     V    ,  as  we  might  at  first  expect;   for 


this  is  forbidden  by  the  law  of  corresponding  points. 
But  we  may  use  a  spectral  image  of  one  eye  to  show 
rotation  of  that  eye. 

Experiment  4-  —  The  manner  in  which  I  conduct 
the  experiment  is  as  follows  :  I  make  a  vertical  spectral 
image  in  the  manner  already  explained  (page  164),  by 
gazing  with  one  eye  (say  the  right)  on  a  vertical  slit  in 

FIG.  65. 


a  closed  window.  I  now  turn  about,  and,  keeping  the 
left  eye  Z,  Fig.  65,  still  shut,  I  look  across  the  root  of 
the  nose  n  with  the  right  eye  R  at  a  perfectly  vertical 
line  w  on  the  wall.  I  see  the  vertical  image  perfectly 
parallel  and  nearly  coincident  with  the  vertical  line  on 
the  wall.  Then,  while  the  right  eye  still  continues  to 
look  along  the  line  P,  s,  I  turn  the  shut  left  eye  L  from 


LAWS   OF  CONVERGENT   MOTION.  187 

its  previous  position  L  s  through  an  angle  of  90°,  until 
its  line  of  sight  is  L  s ' .  In  other  words,  I  run  the 
point  of  sight  or  point  of  convergence  from  the  distant 
point  of  the  wall  w  along  the  line  R  s  to  the  point  a 
near  the  root  of  the  nose.  When  I  do  so,  I  see  the 

spectral  image  incline  to  the  right,  thus —  / ,  indicating 

(since  the  image  is  spectral]  a  rotation  of  the  eye  in  the 
same  direction.  This  experiment  is  very  difficult,  but 
it  is  conclusive. 

Experiment  5. — I  shut  one  eye,  say  the  left,  and 
look  across  the  root  of  the  nose  at  a  distant  object,  as 
in  Fig.  63.  An  assistant  now  observes  attentively  my 
iris,  and  notes  with  care  the  position  of  the  radiating 
lines.  Now,  without  changing  at  all  the  direction  of 
the  line  of  sight,  I  change  the  point  of  sight  to  an  ob- 
ject or  point  very  near  the  root  of  the  nose,  as  in  Fig. 
63,  by  turning  the  optic  axis  of  the  shut  eye  through 
90°.  I  again  relax  the  convergence  so  as  to  make  the 
optic  axes  parallel,  and  again  converge  upon  the  near 
point ;  and  so  on  alternately.  With  every  convergence 
the  iris  is  seen  to  rotate  like  a  wheel  outward.  I  have 
subjected  my  eyes  to  the  observation  of  five  different 
persons,  and  they  all  made  the  same  statement  in  re- 
gard to  the  direction  of  rotation. 

There  can  be  no  longer  any  doubt  that  my  eyes  in 
convergence  rotate  on  the  optic  axes  outward,  the  de- 
gree of  rotation  increasing  with  the  degree  of  conver- 
gence. To  generalize  this  as  a  law  of  ocular  motion  I 
have  found  extremely  difficult,  because  there  are  so  few 
persons  who  are  able  to  verify  the  results,  on  account 
of  imperfect  voluntary  control  of  the  ocular  muscles, 
and  especially  the  difficulty  or  even  impossibility  which 
most  persons  find  in  observing  intelligently  images 


188          DISPUTED   POINTS  IN  BINOCULAR  VISION. 

which  are  not  at  the  point  of  sight.  Nevertheless,  I 
have  found  several  persons  who  by  considerable  prac- 
tice have  been  able  to  confirm  nearly  all  these  experi- 
ments. I  have  also  made  observations  directly  on  the 
eyes  of  other  persons  in  the  manner  described  in  the 
fifth  experiment,  and  noted  the  rotation  of  the  iris 
in  strong  convergence.  I  think,  therefore,  I  am  justi- 
fied in  announcing  the  outward  rotation  of  the  eyes  in 
convergence  as  a  general  law. 

The  Meet  of  Elevation  and  Depression  of  the  Visual 
Plane  on  Rotation. — The  question  next  occurs,  What  is 
the  effect,  on  this  rotation,  of  elevation  or  depression  of 
the  visual  plane  ?  I  have  also  made  many  experiments 
to  determine  this  point. 

Experiment  6. — In  making  experiments  of  this  kind, 
all  that  is  necessary  is  that  the  experimental  plane 
shall  be  exactly  perpendicular  to  the  visual  plane. 
This  may  be  insured  either  by  keeping  the  face  in  its 
former  position  and  changing  the  inclination  of  the 
plane,  or  else,  more  conveniently,  by  fixing  the  plane 
in  its  vertical  position  and  changing  the  inclination 
of  the  face.  If  we  choose  the  latter  method,  then, 
for  experiments  with  the  visual  plane  elevated,  the 
head  or  face  is  turned  downward  and  the  eyes  look 
upward  toward  the  brows  upon  the  experimental  plane 
— care  being  taken  that  the  eyes  in  their  new  position 
shall  be  on  a  level  with  the  center  of  the  plane.  By 
experiments  of  this  kind  I  find  that  the  outward  rota- 
tion in  convergence,  especially  in  strong  convergence, 
increases  decidedly  for  the  same  degree  of  convergence 
with  the  elevation  of  the  visual  plane. 

Experiment  7. — For  experiments  on  rotation  with 
the  visual  plane  depressed,  the  face  must  be  turned  up- 
ward (taking  care  as  before  that  the  eyes  in  their  new 


LAWS  OF  CONVERGENT  MOTION.  189 

position  are  on  a  level  with  the  center  of  the  plane), 
and  then  the  eyes  look  downward  toward  the  point  of 
the  nose  upon  the  experimental  plane.  In  this  case  I 
find  that  for  the  same  degree  of  convergence  the  rota- 
tion decreases  steadily,  until  it  becomes  zero  for  all  de- 
grees of  convergence  when  the  visual  plane  is  depressed 
45°  below  its  primary  position — i.  e.,  when  the  eyes  look 
toward  the  point  of  the  nose.  Below  this  angle  the  ro- 
tation seems  to  be  inverse — i.  e.,  inward — although  it  is 
impossible  to  try  this  with  strong  convergence,  because 
the  nose  is  in  the  way. 

Cause  of  the  Rotation.— It  is  probable  that  the  rota- 
tion is  produced  by  the  action  of  the  inferior  oblique 
muscles.  If  so,  we  can  understand  why  it  increases 
with  elevation  of  the  visual  plane,  and  decreases  with 
its  depression ;  for  in  the  first  case  the  tension  on  theso 
muscles  would  be  increased,  while  in  the  latter  case  it 
would  be  decreased. 

Previous  Researches  on  this  Subject.— The  only  writer 
who  has  to  my  knowledge  made  experiments  on  rotation 
of  the  eyes  in  convergence  is  Meissner.*  The  results  he 
arrives  at  are  substantially  the  same  as  my  own ;  but 
he  arrives  at  them  indirectly,  while  investigating  the 
question  of  the  horopter,  and  by  methods  far  less  exact 
than  those  employed  by  myself.  My  results,  therefore, 
must  be  regarded  as  a  confirmation  and  a  demonstration 
of  his.  Meissner's  method  will  bs  spoken  of  under  the 
head  of  the  horopter. 

Laws  of  Parallel  and  of  Convergent  Motion  Compared. 
— We  will  now  formulate  the  laws  of  convergent  mo- 
tion, and  at  the  same  time  contrast  them  with  those  of 
parallel  motion. 

1.  When  the  eyes  move  in  the  primary  plane  in  the 

*  "Archives  des  Sciences,"  tome  Hi,  1858,  p.  160. 


190  DISPUTED   POINTS   IN   BINOCULAR   VISION. 

same  direction  (parallel  motion),  there  is  no  torsion  •  but 
when  they  move  in  that  plane  in  opposite  directions,  as 
in  convergence,  they  rotate  outward. 

2.  When  the  visual  plane  is  elevated  and  the  eyes 
move  in  the  same  direction  by  parallel  motion,  then 
lateral  motion  to  the  right  produces  torsion  to  the  right, 
and  to  the  left,  torsion  to  the  left;  but  when,  on  the 
contrary,  they  move  in  opposite  directions,  as  in  con- 
vergence, then  as  the  right  eye  moves  to  the  left,  i.  e., 
toward  the  nose,  it  rotates  to  the  right,  and  as  the  left 
eye  moves  toward  the  nose,  i.  e.,  to  the  right,  it  rotates 
to  the  left.     If  Listing's  law  operated  at  all  in  this  case, 
as  it  acts  in  the  opposite  direction,  it  would  tend  to 
neutralize  the  effects  of  convergent  rotation ;  but  such 
is  not  the  fact.     On  the  contrary,  as  we  have  seen,  the 
outward  rotation  increases  with  elevation  of  the  visual 
plane. 

3.  When  the  visual  plane  is  depressed,  and  the  eyes 
move  from  side  to  side  by  parallel  motion,  then  lateral 
motion  to  the  right  is  attended  with  torsion  to  the  left, 
and  motion  to  the  left  with  torsion  to  the  right.     Also 
when  the  eyes  move  by  convergent  motion  in  opposite 
directions,  they  rotate  in  the  same  direction  as  in  the 
case  of  parallel  motion ;  but  there  is  this  great  differ- 
ence :  that  while  in  parallel  motion  the  torsion  increases 
with  the  angle  of  depression,  in  convergent  motion  it 
decreases  to  zero  at  45°.     If  Listing's  law  operated  at 
all  in  this  case,  it  would  cooperate  with  and  increase 
the  effect  of  convergent  motion ;  but  the  very  reverse 
is  the  fact,  the  rotation  decreasing  with  the  angle  of 
depression. 

4.  We  have  already  shown  that  the  so-called  torsion 
of  parallel  motion  is  not  a  true  rotation  on  the  optic 
axes,  but  only  an  apparent  rotation,  the  result  of  refer- 


LAWS  OF  CONVERGENT  MOTION. 

ence  to  a  new  spatial  meridian  not  parallel  with  the 
primary  meridian.  On  the  contrary,  the  rotation  pro- 
duced by  convergent  motion  is  a  true  rotation  on  the 
optic  axes,  as  shown  by  the  fact  that  one  eye  without 
change  of  position  will  rotate  in  sympathy  with  the 
convergent  motion  of  the  other  eye  (experiments  4 
and  5). 

It  is  evident,  then,  that  when  the  eyes  move  in  the 
same  direction  parallel  to  each  other,  as  in  ordinary 
vision  of  distant  objects,  then  all  their  motions  are  gov- 
erned by  Listing's  law ;  but  when,  on  the  contrary,  they 
move  in  opposite  directions,  as  in  convergence,  then  the 
law  of  Listing  is  wholly  abrogated,  or  else  overborne, 
and  another  law  reigns  in  its  place. 


CHAPTEE  II. 

THE     HOROPTER. 

IF  we  look  at  any  point,  the  two  visual  lines  con- 
verge and  meet  at  that  point.  Its  two  images  therefore 
fall  on  corresponding  points  of  the  two  retinae,  viz.,  on 
their  central  spots.  A  small  object  at  this  point  of 
convergence  is  seen  absolutely  single.  We  have  called 
this  point  "  the  point  of  sight."  All  objects  beyond  or 
on  this  side  the  point  of  sight  are  seen  double — in  the 
one  case  homonyrnously,  in  the  other  heteronymously 
— because  their  images  do  not  fall  on  corresponding 
points  of  the  two  retinae.  But  objects  below  or  above, 
or  to  one  side  or  the  other  side  of  the  point  of  sight, 
may  possibly  be  seen  single  also.  The  sum  of  all  the 
points  which  are  seen  single  while  the  point  of  sight 
remains  unchanged  is  called  the  horopter. 

Or  it  may  be  otherwise  expressed  thus :  Each  eye 
projects  its  own  retinal  images  outward  into  space,  and 
therefore  has  its  own  field  of  view  crowded  with  its  own 
images.  When  we  look  at  any  object,  we  bring  the 
two  external  images  of  that  object  together,  and  super- 
pose them  at  the  point  of  sight.  Now  the  point  of 
sight,  together  with  the  images  of  all  other  objects  or 
points  which  coalesce  at  that  moment,  lie  in  the  horop- 
ter. The  images  of  all  objects  lying  in  the  horopter 


THE  HOROPTER.  193 

fall  on  corresponding  points,  and  are  seen  single ;  and 
conversely,  the  horopter  is  the  surface  (if  it  be  a  surface) 
of  single  vision. 

Is  the  horopter  a  surface,  or  is  it  only  a  line  f  In 
either  case,  what  are  its  form  and  position  ?  These  ques- 
tions have  tasked  the  ingenuity  of  physicists,  mathemati- 
cians, and  physiologists.  If  the  position  of  correspond- 
ing points  were  certainly  known,  and  invariable  in  ref- 
erence to  a  given  spatial  meridian,  then  the  question  of 
the  horopter  would  be  a  purely  mathematical  one.  But 
the  position  of  corresponding  points  may  change  in 
ocular  motions.  It  is  evident,  then,  that  it  is  only  on 
an  experimental  basis  that  a  true  theory  of  the  horopter 
can  be  constructed.  And  yet  the  experimental  deter- 
mination, as  usually  attempted,  is  very  unsatisfactory 
on  account  of  the  indistinctness  of  perception  of  objects 
except  very  near  the  point  of  sight.  Therefore  experi- 
ments determining  the  laws  of  ocular  motion,  and 
mathematical  reasoning  based  upon  these  laws,  seem  to 
be  the  only  sure  method. 

The  most  diverse  views  have  therefore  been  held  as 
to  the  nature  and  form  of  the  horopter.  Aguilonius,  the 
inventor  of  the  name,  believed  it  to  be  a  plane  passing 
through  the  point  of  sight  and  perpendicular  to  the 
median  line  of  sight.  Others  have  believed  it  to  be  the 
surface  of  a  sphere  passing  through  the  optic  centers 
and  the  point  of  sight;  others,  a  torus  generated  by 
the  revolution  of  a  circle  passing  through  the  optic 
centers  and  the  point  of  sight,  about  a  line  joining  the 
optic  centers.  The  subject  has  been  investigated  with 
great  acuteness  by  Prevost,  Miiller,  Meissner,  Claparede, 
and  finally  by  Helmholtz.  Prevost  and  Miiller  deter- 
mine in  it,  as  they  think,  the  circumference  of  a  circle 
passing  through  the  optic  centers  and  the  point  of  sight. 


194:          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

(the  horopteric  circle),  and  a  line  passing  through  the 
point  of  sight  and  perpendicular  to  the  plane  of  the 
circle  (horopteric  vertical).  The  horopteric  circle  of 
Miiller  is  shown  in  Fig.  66,  in  which  0  0'  is  the  line 
between  the  optic  centers,  n  nf  the  nodal  points  or 
points  of  ray-crossing,  A  the  point  of  sight,  and  B  an 


FIG.  66. 


object  to  the  left  and  situated  in  the  circumference 
of  the  circle.  Of  course,  the  images  of  A  fall  on  the 
central  spots  c  cf.  It  is  seen  also  that  the  images  of  B 
fall  at  &  5',  at  equal  distances  from  the  central  spots 
c  cf,  one  on  the  nasal  half  and  one  on  the  temporal  half, 
and  therefore  on  corresponding  points.  The  Jioropteric 
vertical  of  Miiller  passes  through  A  and  perpendicular 
to  the  plane  of  the  circle  (i.  e.,  of  the  diagram). 

Claparede  makes  the  horopter  a  surface,  of  such  a 
form  that  it  contains  a  straight  line  passing  through  the 
point  of  sight  and  perpendicular  to  the  visual  plane,  and 


THE  HOROPTER. 


195 


FIG.  67. 


also  such  that  every  plane  passing  through  the  optic  cen- 
ters makes  by  intersection  with  this  surface  the  circum- 
ference of  a  circle.  In  other  words,  he  thinks  that  the 
horopter  is  a  surface 
which  contains  the  ho- 
ropteric  vertical,  B  A. 
Bf,  Fig.  67,  and  the  ho- 
ropteric  circle,  0  A  O', 
and  in  addition  is  fur- 
ther characterized  by 
the  fact  that  the  inter- 
section with  it  of  every 
plane  passing  through 
the  optic  centers  0  0' 
upward  as  0  B  0'  or 
downward  as  0  B'  0'  is 
also  a  circle.  It  is  evi- 
dent that,  as  these  cir- 
cles increase  in  size  up- 
ward and  downward, 
the  horopter  according 
to  Claparede  is  a  surface  of  singular  and  complex 
form. 

Helmholtz  arrives  at  results  entirely  different.  Ac- 
cording to  him,  the  horopter  varies  according  to  the 
position  of  the  point  of  sight,  and  is  therefore  very 
complex.  He  sums  up  his  conclusions  thus  :  * 

"  1.  Generally  the  horopter  is  a  line  of  double  cur- 
vature produced  by  the  intersection  of  two  hyperbo- 
loids,  which  in  some  exceptional  cases  may  be  changed 
into  a  combination  of  two  plane  curves. 

"  2.  For  example,  where  the  point  of  convergence 

*  Croonian  Lecture,  in  "  Proceedings  of  the  Royal  Society,"  xiii  (1864), 
p.  197 ;  also  "  Optique  Physiologique,"  p.  901  et  seq. 


196          DISPUTED   POINTS  IN  BINOCULAR  VISION.       . 

(point  of  sight)  is  situated  in  the  median  plane  of  the 
head,  the  horopter  is  composed  of  a  straight  line  drawn 
through  the  point  of  convergence,  and  a  conic  section 
going  through  the  optic  centers  and  intersecting  the 
straight  line. 

"  3.  ^When  the  point  of  convergence  is  situated  in 
the  plane  which  contains  the  primary  directions  of  both 
visual  lines  (primary  visual  plane),  the  horopter  is  com- 
posed of  a  circle  going  through  that  point  and  through 
the  optic  centers  (horopteric  circle),  and  a  straight  line 
intersecting  the  circle. 

"4.  When  the  point  of  convergence  is  situated  both 
in  the  middle  plane  of  the  head  and  in  the  primary 
visual  plane,  the  horopter  is  composed  of  the  horopteric 
circle  and  of  a  straight  line  going  through  that  point. 

"  5.  There  is  only  one  case  in  which  the  horopter  is 
a  plane,  namely :  when  the  point  of  convergence  is  sit- 
uated in  the  middle  plane  of  the  head  and  at  an  infinite 
distance.  Then  the  horopter  is  a  plane  parallel  to  the 
visual  lines,  and  situated  beneath  them  at  a  distance 
which  is  nearly  as  great  as  the  distance  of  the  feet  of 
the  observer  from  his  eyes  when  he  is  standing.  There- 
fore, when  we  look  straight  forward  at  a  point  on  the 
horizon,  the  horopter  is  a  horizontal  plane  going  through 
our  feet ;  it  is  the  ground  on  which  we  stand. 

"  6.  When  we  look  not  at  an  infinite  distance,  but 
at  any  point  on  the  ground  on  which  wre  stand  which 
is  equally  distant  from  the  two  eyes,  the  horopter  is  not 
a  plane,  but  the  straight  line  wrhich  is  one  of  its  parts 
coincides  with  the  ground." 

Some  attempts  have  been  made  to  establish  the 
existence  of  the  horopteric  circle  of  Miiller  by  means 
of  experiments.  A  plane  is  prepared  and  pierced  with 
a  multitude  of  holes  into  wrhich  pegs  may  be  set.  The 


THE  HOROPTER.  197 

eyes  look  horizontally  over  tlie  plane  on  one  peg,  and 
the  others  are  arranged  in  such  wise  that  they  appear 
single.  It  is  found  that  they  must  be  arranged  in  a 
circle.  I  have  tried  repeatedly,  but  in  vain,  to  verify 
this  result.  The  difficulty  is  the  extreme  indistinctness 
of  perception  at  any  appreciable  distance  from  the  point 
of  sight.  But,  as  a  general  fact,  the  results  reached  by 
the  observers  thus  far  mentioned  have  been  reached  by 
the  most  refined  mathematical  calculations,  based  on 
certain  premises  concerning  the  position  of  correspond- 
ing points  and  on  the  laws  of  ocular  motion.  We  will 
examine  only  those  of  Helmholtz,  as  being  the  latest 
and  most  authoritative. 

Helmholtz's  results  are  based  upon  the  law  of  Lis- 
ting as  governing  all  the  motions  of  the  eye,  and  upon 
his  own  peculiar  views  concerning  the  relation  between 
what  he  calls  the  apparent  and  the  real  vertical  me- 
ridian of  the  retina.  The  real  vertical  meridian  of  the 
eye  is  the  line  traced  on  the  retina  by  the  image  of  a 
really  vertical  linear  object  when  the  median  plane  of 
the  head  is  vertical  and  the  eye  in  the  primary  position. 
The  apparent  vertical  meridian  of  the  eye  is  the  line 
traced  by  the  image  of  an  apparently  vertical  linear 
object  in  the  same  position  of  the  eye.  This  is  also 
called  the  vertical  line  of  demarcation,  because  it  di- 
vides the  retina  into  two  halves  which  correspond  each 
to  each  and  point  for  point.  Now,  according  to  Helm- 
holtz, the  apparent  vertical  meridian  or  vertical  line 
of  demarkation  does  not  coincide  with  the  real  vertical 
meridian,  but  makes  with  it  in  each  eye  an  angle  of 
1J°,  and  therefore  with  one  another  in  the  two  eyes  of 
2J°.  The  horizontal  meridians  of  the  eyes,  both  real 
and  apparent,  coincide  completely.  Therefore,  if  the 
two  eyes  were  brought  together  in  such  wise  that  their 


198  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

real  vertical  and  horizontal  meridians  should  coincide, 
their  apparent  horizontal  meridians  would  also  coin- 
cide ;  but  the  apparent  vertical  meridians  would  cross 

l\r 

each   other  at  the  central  spot   thus —     V    ,  making 

r/\l 

an  angle  of  2^°.  For  this  reason  a  perfectly  vertical 
line  will  appear  to  the  right  eye  not  vertical,  but  in- 
clined to  the  left,  and  to  the  left  eye  inclined  to  the 
right.  In  order  that  a  line  shall  appear  perfectly  ver- 
tical to  one  eye,  it  must  incline  for  the  right  eye  1J° 
to  the  right,  and  for  the  left  1J°  to  the  left.  But  a 
horizontal  line  appears  truly  horizontal.  Therefore  an 
upright  rectangular  cross  will  appear  to  the  right  eye 

thus — ,  and  to  the  left  eye  thus 1 — .     The 

inclination  of  these  lines  is,  however,  exaggerated.  If, 
therefore,  according  to  Helmholtz,  we  make  a  diagram 
of  which  one  half  is  composed  of  black  lines  on  white 
ground,  and  the  other  of  white  lines  on  black  ground, 
like  those  already  used,  but  in  which,  while  the  hori- 
zontals run  straight  across  horizontally,  the  verticals  on 
the  right  half  are  inclined  1J°  to  the  right,  and  on  the 
left  half  the  same  amount  to  the  left  (Fig.  68),  then,  on 
combining  these  by  gazing  beyond  the  plane  of  the  dia- 
gram (i.  e.,'with  parallel  eyes),  either  writh  the  naked 
eye  or  with  the  stereoscope,  the  verticals  will  be  seen 
to  come  together  parallel  and  unite  perfectly. 

Now  Helmholtz's  views  of  the  form  of  the  horopter 
are  based  wholly  on  this  supposed  relation  of  real  and 
apparent  vertical.  Take  for  example  his  case  of  the 
eyes  fixed  on  a  distant  point  on  the  horizon.  In  this 
case,  he  says,  "  the  horopter  is  the  ground  on  which  we 
stand."  This  is  true  if  the  relation  above  mentioned  is 


THE   HOROrTER. 


199 


true  ;  for,  with  an  interocular  distance  of  2£  inches,  two 
lines  drawn  through  the  optic  centers,  each  inclined  1  J° 
with  the  vertical  and  therefore  2J°  with  each  other, 


200  DISPUTED  POINTS  IN   BINOCULAR  VISION. 

would  in  fact  meet  about  5  feet  below — i.  e.,  about  the 
feet.  If,  therefore,  we  place  two  actual  rods  together 
on  the  ground  between  the  feet,  and  the  upper  ends  be- 
fore the  pupils,  the  eyes  being  parallel,  it  is  evident  that 
the  image  of  the  right  rod  on  the  right  retina  and  that 
of  the  left  rod  on  the  left  retina  would  fall  exactly  on 
Helmholtz's  apparent  vertical  meridian,  and,  if  Helm- 
holtz's views  be  correct,  on  the  vertical  lines  of  demar- 
kation  and  on  corresponding  points  of  the  retinse,  and 
thus  would  be  bin  ocularly  combined  and  seen  as  a  single 
line  lying  along  the  ground  to  infinite  distance.  And 
conversely,  with  the  eyes  parallel  and  the  lines  of  de- 
markation inclined  1J°  with  the  vertical,  a  rod  lying  on 
the  ground  to  infinite  distance  would  cast  its  images  on 
these  lines,  and  therefore  be  seen  single  throughout. 

There  are  several  curious  questions  which  force  them- 
selves on  our  attention  here  if  Helmholtz's  view  be  true. 

1.  If  we  suppose  the  two  eyes  to  be  placed  one  on  the 
v  fiQ  other,  so  that  the  real  vertical  meridians 

Jr  IG.  by. 

coincide,  we  have  already  seen  that 
Helmholtz's  apparent  verticals  or  lines 
of  demarkation  will  cross  each  other 
like  an  X,  as  in  Fig.  69,  making  with 
each  other  an  angle  of  2|°.  ~Now  the 
twro  rods  2£  inches  apart  at  the  height 
of  the  eyes,  and  meeting  below  at  the 
THE  BETING  SUPERPOSED,  feet,  or  the  rod  lying  along  the  ground 

-r  r,  line  of  demarka-    t     infinite  distance,  WOuld  OCCUpV  with 
tion  of  right  eye ;   II,  *« 

line  of  demarkation  of  their  images  only  the  upper  half  of 
the  X.  But  suppose  the  two  rods,  in- 
stead of  stopping  opposite  the  eyes,  to  continue  upward 
to  the  limits  of  the  field  of  view.  Obviously  this  upper 
half  would  cast  images  on  the  lower  half  of  the  X,  and 
therefore  would  be  seen  single  also.  Where  shall  we 


THE  HOROPTER.  201 

refer  them  ?  Or,  to  express  it  differently,  the  horopter 
with  the  eyes  looking  at  a  distant  horizon,  according  to 
Helmholtz,  is  the  ground  we  stand  on ;  but  this  is  evi- 
dently pictured  on  the  upper  halves  only  of  the  two 
retinae.  Where  is  the  other  half  of  the  horopter  cor- 
responding to  the  lower  halves  of  the  retinae  ? 

2.  Again :  According  to  Helmholtz,  in  looking  at 
a  distance  the  horopter  is  the  ground  we  stand  on,  and 
he  gives  this  as  the  reason  why  distance  along  the 
ground  is  more  clearly  perceived  than  in  other  posi- 
tions.* On  the  contrary,  it  seems  to  me  that  it  would 
have  just  the  reverse  effect.  If  the  horopter  were  the 
ground  we  stand  on,  then  relative  distances  on  the 
ground  could  not  be  perceived  by  binocular  perspec- 
tive at  all ;  for  this  is  wholly  dependent  on  the  exist- 
ence of  double  images,  which  could  not  occur  in  this 
case  by  the  definition  of  the  horopter.  It  would  be 
therefore  only  by  other  forms  of  perspective  that  we 
could  distinguish  relative  distance  along  the  ground. 
But  that  we  do  perceive  perspective  of  the  ground 
binocularly — i.  e.,  by  double  images — is  proved  by  the 
fact  that  the  perspective  of  the  receding  ground  is  very 
perfect  in  stereoscopic  pictures,  where  the  images  of 
nearer  points  are  necessarily  double ;  for  the  camera 
has  no  such  distinction  between  real  and  apparent  ver- 
ticality  as  Helmholtz  attributes  to  the  eye. 

But  it  is  useless  to  argue  the  point  any  further,  for 
I  am  quite  sure  that  the  property  which,  Helmholtz 
finds  in  his  eye  is  not  general,  and  therefore  not  nor- 
mal. We  have  seen  that  in  convergence  the  eyes  ro- 
tate outward,  so  as  to  bring  about  the  very  condition  of 
things  temporarily  which  Helmholtz  finds  permanent 
in  his  eyes.  I  have  therefore  thought  it  possible,  or 

~~ 


202          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

even  probable,  that  the  same  habits  in  early  life  which, 
by  constant  adapting  of  the  eyes  to  vision  of  near  ob- 
jects, finally  produce  myopy,  may  also,  by  constant 
slight  rotation  of  the  eyes  outward  and  distortion  in 
convergence  on  near  objects,  finally  bring  about  a  per- 
manent condition  of  slight  distortion  and  outward  rota- 
tion of  1J°.  Helmholtz  is  slightly  myopic.* 

However  this  may  be,  I  am  sure  there  is  no  such 
relation  between  real  and  apparent  vertical  meridian  in 
my  eyes  as  that  spoken  of  by  Helmholtz.  All  the  ex- 
periments supposed  to  prove  such  relation  fail  complete- 
ly with  me.  A  vertical  rectangular  cross  appears  rectan- 
gular to  either  eye.  The  lines  of  Helmholtz's  diagram, 
Fig.  66,  when  combined  beyond  the  plane  of  the  dia- 
gram, either  by  the  naked  eyes  or  by  a  stereoscope,  do 
not  come  together  parallel,  but  with  a  decided  angle, 
viz.,  1J°.  But  when  I  turn  the  diagram  upside  down, 
and  combine  by  squinting,  then  the  vertical  lines,  being 
inclined  the  other  way,  as  in  my  diagram,  Fig.  61,  com- 
bine perfectly  by  outward  rotation  of  the  eyes.  I  have 
constructed  other  diagrams  with  less  and  less  inclination 
of  the  verticals,  until  the  inclination  was  only  10',  and 
still  I  detected  the  want  of  parallelism  when  combined 
beyond  the  plane  of  the  diagram.  Beyond  this  limit 
I  could  not  detect  it,  but  I  believe  only  because  the 
limit  of  perception  was  passed ;  for  when  the  lines  are 
made  perfectly  vertical,  they  come  together  perfectly 
parallel  and  unite  absolutely.  It  is  certain,  therefore, 
that  in  my  eyes  the  vertical  line  of  demarkation  coin- 
cides completely  with  the  true  vertical  meridian. 

Meissnerf  alone,  of  all  writers  with  whom  I  am 

*  Op.  dt.,  p.  914. 

f  Meissner,  "Physiologic  des  Sehorgans";  also  "Archives  des  Sci- 
ences," vol.  iii  (1858),  p.  160. 


THE  HOROPTER.  203 

acquainted,  attempts  to  determine  the  horopter  by  ex- 
periment. According  to  him,  if  a  stretched  thread  be 
held  in  the  median  plane  at  right  angles  to  the  primary 
visual  plane,  about  6  to  8  inches  distant,  and  the  point 
of  sight  be  directed  on  the  middle,  the  thread  will  not 
appear  single,  but  the  two  images  will  cross  each  other 

r\ll 
at  the  point  of  sight  thus —    V    ,  r  r  being  the  right- 

l'!\r' 

eye  image,  and  I  I'  the  left-eye  image.  Now,  as  the 
images  are  heteronymous  at  the  upper  end  and  homo- 
nymous  at  the  lower  end,  it  is  evident  that  they  will 
unite  at  some  farther  point  above  and  some  nearer  point 
below.  By  inclining  the  thread  in  the  manner  indi- 
cated— i.  e.,  by  carrying  the  upper  end  farther  and 
bringing  the  lower  end  nearer — the  two  images  come 
together  more  and  more,  until  at  a  certain  angle  of  in- 
clination, varying  with  the  distance  of  the  point  of  sight, 
they  unite  perfectly.  The  thread  is  now  in  the  horopter. 
Experiment. — I  find  that  the  best  way  to  succeed 
with  Meissner's  experiment  is  as  follows :  Hold  a 
stretched  black  thread  parallel  with  the  surface  of  the 
glass  of  an  open  window,  and  within  half  an  inch  of 
it.  Now,  with  the  eyes  in  the  primary  position,  look, 
not  at  the  thread,  but  at  some  spot  on  the  glass.  It 
will  be  seen  that  the  double  images  of  the  thread  are 
not  parallel,  but  make  a  small  angle  with  each  other, 

r\  I1 
thus —  \  /  .     Now  bring  the  lower  end  nearer  the  ob- 


server very  gradually.  It  will  be  seen  that  the  double 
images  become  more  and  more  nearly  parallel,  until 
at  a  certain  angle  of  inclination  the  parallelism  is  per- 
fect. I  have  made  several  experiments  with  a  view 
to  measuring  the  angle  of  inclination  for  different  dis- 


204: 


DISPUTED  POINTS  IN   BINOCULAR  VISION. 


tances  of  the  point  of  sight.  I  find  that  for  8  inches 
the  inclination  is  .about  7°  or  8° ;  for  4  inches,  about 
8°  or  9°.  It  seems  to  increase  as  the  point  of  sight  is 
nearer.  But  of  this  increase  subsequent  experiments 
make  me  doubtful. 

Meissner's  results  may  be  summarized  thus : 

1.  With  the  eyes  in  the  primary  position  and  the 
point  of  sight  at  infinite  distance,  the  horopter  is  a 
plane  perpendicular  to  the  median  line  of  sight  (plane 
of  Aguilonius). 

2.  For  every  nearer  point  of  sight  in  the  primary 
plane,  the  horopter  is  not  a  surface  at  all,  but  a  line 
inclined  to  the  visual  plane  and  dipping  toward  the 
observer,  the  inclination  increasing  with  the  nearness 
of  the  point  of  sight  or  degree  of  convergence. 

3.  In  turning  the  plane  of  vision  upward,  the  in- 
clination of  the  horopteric  line  increases.     In  turning 
the  plane  of  vision  downward,  the  inclination  of  the 
horopteric  line  decreases,  until  it  becomes  zero  at  45°, 
and  the  horopteric  line  expands  into  a  plane  passing 
through  the  point  of  sight  and  perpendicular  to  the 
median  visual  line. 

Furthermore,  Meissner  attributes  these  results  to  a 
rotation  of  the  eyes  on  the  optic  or  visual  axes  outward / 

FIG.  70. 


so  that  the  vertical  lines  of  demarkation,  C  7),  C'  D' , 
Fig.  TO,  no  longer  coincide  perfectly  with  the  vertical 


THE   HOROPTER.  205 

meridians  A  B,  A'  B' ,  nor  the  horizontal  lines  of  de- 
markation  G  H,  G '  H'  with  the  horizontal  meridians 
E  F,  E'  F',  as  they  do  when  the  eyes  are  parallel,  hut 
cross  them  at  a  small  angle.  With  eyes  parallel,  the 
images  of  a  vertical  line  will  fall  on  the  vertical  lines  of 
demarkation  (for  these  then  coincide  with  the  vertical 
meridians)  and  be  seen  single.  But  if  the  eyes  rotate 
outward  in  convergence,  then  the  images  of  a  vertical 
line  will  no  longer  fall  on  the  vertical  lines  of  demar- 
kation, and  therefore  will  be  seen  double  except  at  the 
point  of  sight.  In  order  that  the  image  of  a  line  shall 
fall  on  the  vertical  lines  of  demarkation  and  be  seen 
single,  with  the  eyes  in  this  rotated  condition,  the  line 
must  not  be  vertical,  but  inclined  with  the  upper  end 
farther  away  and  the  lower  end  nearer  to  the  observer. 
It  is  evident  also  that  under  these  circumstances  the 
horopter  can  not  be  a  surface,  but  is  restricted  to  a  line. 
This  requires  some  explanation. 

If  the  eyes  be  converged  on  a  vertical  line,  and  then 
rotated  on  their  optic  axes,  as  we  have  seen,  the  line 
will  be  doubled  except  at  the  point  of  sight.  This 
doubling  is  the  result  of  horizontal  displacement  of  the 
two  images  in  opposite  directions  at  the  two  ends — the 
upper  ends  heteronymously,  the  lower  ends  homony- 
mously.  Now,  since  heteronymous  images  unite  by  car- 
rying the  object  farther  away  and  homonymous  images 
by  bringing  it  nearer,  it  is  evident  that  if  the  line  be  in- 
clined by  carrying  the  upper  end  farther  and  bringing  the 
lower  end  nearer,  the  two  images  will  unite  completely, 
and  thus  form  a  horopteric  line.  But  all  points  to  the 
right  or  left  of  this  horopteric  line  will  also  double  by 
rotation  of  the  eyes ;  but  this  doubling  is  by  vertical 
displacement,  as  shown  in  Fig.  70.  Now  doubling  by 
vertical  displacement  can  not  be  remedied  by  increasing 


206 


DISPUTED  POINTS  IN  BINOCULAR  VISION. 


FIG.  71. 


or  decreasing  distance,  because  the  eyes  are  separated 
horizontally.  It  is  therefore  irremediable.  Hence  no 
form  of  surface  can  satisfy  the  conditions  of  single 
vision  right  and  left  of  the  horopteric  line.  Hence, 
also,  the  restriction  of  the  horopter  to  a  line,  and  the 
inclination  of  that  line  on  the  plane  of  vision,  are  ne- 
cessary consequences  of  the  rotation  of  the  eyes  on 
their  viusal  axes.  This  rotation  I  have  already  proved 
in  the  most  conclusive  manner  by  experiments  detailed 
in  the  last  chapter. 

It  will  be  seen  by  reference  to  the  preceding  chap- 
ter that  rny  results  coincide  perfectly  with  those  of 
Meissner,  although  I  was  ignorant  of  Meissner's  re- 
searches when  I  commenced  my  experiments  many 
years  ago.  The  end  in  view  in  the 
two  cases,  and  also  the  methods 
.used,  wrere  different.  Meissner  was 
investigating  the  question  of  the 
horopter,  and  outward  rotation  of 
the  eyes  was  the  logical  inference 
from  the  position  of  the  horopter 
discovered  by  him.  I  was  investi- 
gating the  laws  of  convergent  mo- 
tion, and  the  nature  of  the  horopter 
was  a  logical  consequence  of  the  out- 
ward rotation  which  I  discovered. 
Meissner's  method  is,  however,  far 
less  refined  and  exact  than  mine. 

I  have  also  proved  the  inclina- 
tion of  the  horopteric  line  by  direct 
experiments  by  my  method. 
Experiment  1. — If  two  lines,  one  black  on  white 
and  the  other  white  on  black,  be  drawn  with  an  in- 
clination of  1J°  with  the  vertical,  and  therefore  2^° 


THE   HOROPTER. 


207 


with  each  other,  and  the  eyes  be  brought  so  near  to  any 
points  a  a,  Fig.  71  (taking  care  that  the  visual  plane 
shall  be  perpendicular  to  the  plane  of  the  diagram), 
that  these  shall  unite  beyond  the  plane  of  the  diagram 
at  the  distance  of  7  inches,  the  two  lines  will  coincide 
perfectly.  If  then  the  diagram  be  turned  upside  down, 
and  the  lines  be  again  united  by  squinting — the  dia- 
gram being  in  this  case  a  little  farther  off,  so  that  the 
point  of  sight  shall  again  be  7  inches — the  coincidence 
of  the  lines  will  be  again  perfect.  Fig.  72 — in  which 
R  and  L  represent  the  right  and  left  eyes  respectively, 


FIG.  72. 


H 


a  H  and  a!  II  the  lines  to  be  combined  in  these  two 
positions,  and  A  the  point  of  sight — will  explain  how 
the  combination  takes  place.  The  line  H  A  H  is  the 
horopteric  line. 

This  experiment  is  difficult  to  make,  but  I  am  quite 
confident  of  the  reliability  of  the  results  reached.  I 
made  many  experiments  with  different  degrees  of  in- 
clination of  the  lines  a  H,  a'  H,  and  therefore  with 
different  degrees  of  convergence,  and  many  calculations 
based  on  these  experiments,  to  determine  the  inclination 
of  the  horopteric  line  for  different  degrees  of  conver- 
gence. But  the  experiments  are  so  difficult  that,  while 


208 


DISPUTED  POINTS  IN  BINOCULAR  VISION. 


in  every  case  the  inclination  of  the  horopteric  line  was 
proved,  the  exact  angle  could  not  be  made  out  with 
certainty.  It  seemed  to  me  about  7°  for  all  degrees  of 
convergence,  and  therefore  for  all  distances.  It  cer- 
tainly does  not  seem  to  increase  with  the  degree  of  con- 
vergence, as  maintained  by  Meissner. 

Experiment  2. — I  next  adopted  another  and  I  think 
a  better  method.  I  used  a  plane  and  diagram  covered 
with  true  verticals  only,  as  in  Fig.  73.  I  placed  this, 
instead  of  vertical  as  in  previous  experiments,  inclined 

FIG.  73. 


7°,  and  therefore  in  the  supposed  position  of  the  horop- 
ter.  Placing  the  face  in  a  vertical  position  and  the 
plane  of  vision  horizontal — i.  e.,  my  eyes  at  the  same 
height  as  the 'little  circles — I  combined  these  succes- 
sively, and  watched  how  the  lines  came  together.  I 
found  that  when  inclined  7°  all  the  lines,  even  the  far- 
thest apart — viz.,  30  inches — came  together  perfectly 
parallel.  I  then  tried  the  plane  inclined  8° ;  the  par- 
allelism was  still  complete  for  all  degrees  of  conver- 
gence. But  when  the  plane  was  inclined  9°,  the  in- 
clination of  the  lines  in  coming  together  successively 


THE  HOROPTER. 


209 


was  distinctly  perceptible.     I  am  sure  therefore  that 
the  true  inclination  is  about  7°  or  8°. 

Such  are  the  phenomena ;  now  for  the  interpretation. 
It  will  be  observed  that  when  the  plane  represented  by 
the  diagram  fig.  73  is  inclined  to  the  visual  plane,  all 
the  vertical  lines  converge  by  perspective ;  the  conver- 
gence increasing  with  the  distance  from  the  central  line, 
as  in  Fig.  74,  which  represents  such  an  inclined  plane 
referred  to  a  plane  perpendicular  to  the  visual  plane. 
By  calculation  and  careful  plotting,  I  find  that  at  the 

FIG.  74. 


PROJECTION  OF  PLANE  INCLINED  8°. 

distance  of  15  inches  the  convergence  of  the  first  two 
lines,  6  inches  apart,  for  a  plane  inclined  8°,  is  each 
about  1°  31',  or  to  each  other  3°  2' ;  of  the  second  pair, 
12  inches  apart,  3°  3'  each,  or  6°  6'  to  each  other;  of 
the  third  pair,  18  inches  apart,  4°  35'  each,  or  9°  10' 
to  each  other ;  of  the  fourth  pair,  24  inches  apart,  6°  7' 
each,  or  12°  14'  to  each  other ;  of  the  fifth  pair,  30  inches 
apart,  7°  40'  each,  or  15°  20'  to  each  other.  Therefore, 
an  increasing  rotation  of  the  eyes  outward  is  necessary 
to  bring  these  together  parallel.  The  distance  of  the 
point  of  sight  measured  from  the  optic  centers  varied 


210          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

from  4J  inches  in  the  first  to  1J  inch  in  the  last  case ; 
but  the  inclination  of  the  horopteric  line  was  the  same 
in  every  case.  This  is  probably  the  most  accurate  means 
of  determining  by  direct  experiment  both  the  horopter 
and  the  degree  of  rotation  of  the  eyes  for  every  degree 
of  convergence  of  the  optic  axes. 

Experiment  3. — I  next  tried  the  same  experiment 
with  the  visual  plane  depressed  45°,  but  yet  perfectly 
horizontal.  In  this  position,  on  combining  the  vertical 
lines,  I  find  that  they  retain  perfectly  their  natural  per- 
spective convergence.  On  decreasing  the  inclination 
of  the  diagram  the  perspective  convergence  becomes 
less  and  less,  until  when  the  plane  of  the  diagram  is 
vertical  the  lines  come  together  again  parallel  for  all 
degrees  of  convergence,  as  already  found  in  the  previ- 
ous experiment.  I  conclude  therefore  that  in  turning 
the  visual  plane  downward  the  inclination  of  the  horop- 
teric line  becomes  less  and  less,  until  when  the  visual 
plane  is  depressed  45°  it  becomes  perpendicular  to  that 
plane,  and  at  the  same  time  expands  to  a  surface. 

In  turning  the  visual  plane  upward,  I  find,  espe- 
cially for  high  degrees  of  convergence,  that  I  must  in- 
cline the  plane  of  the  diagram  more  than  8°  (viz.,  about 
10°)  in  order  that  the  lines  shall  come  together  parallel. 
From  this  I  conclude  a  higher  degree  of  rotation  of  the 
eyes  and  a  higher  inclination  of  the  horopteric  line. 

The  points  on  which  I  do  not  confirm  Meissner  are : 
1.  The  increasing  inclination  of  the  horopteric  line  with 
increasing  nearness  of  the  point  of  sight.  I  make  it 
constant.  2.  I  think  it  probable  also  that  Meissner  is 
wrong  in  supposing  that  the  horopter,  when  the  visual 
plane  is  depressed  45°,  is  a  plane.  It  is  certainly  a  sur- 
face, but  not  a  plane ;  for  it  is  geometrically  clear  that 
points  in  a  perpendicular  plane  to  the  right  or  left  of 


THE  HOROPTER.  211 

the  point  of  sight  can  not  fall  on  corresponding  points  of 
the  two  retinoe.  The  horopter  in  this  case  is  evidently 
a  curved  surface.  I  do  not  undertake  to  determine  its 
nature  by  mathematical  calculation,  and  the  experimen- 
tal investigation  is  unsatisfactory  for  the  reason  already 
given,  viz.,  the  extreme  indistinctness  of  perception  of 
points  situated  any  considerable  distance  from  the  point 
of  sight  in  any  direction. 

In  regard  to  the  horopter  I  consider  the  following 
points  to  be  well  established : 

1.  As  a  necessary  consequence  of  the  outward  rota- 
tion of  the  eyes  in  convergence,  for  all  distances  in  the 
primary  visual  plane  the  horopter  is  a  line  inclined  to 
the  visual  plane,  the  lower  end  nearer  the  observer. 
But  whether  the  inclination  is  constant,  or  increases  or 
decreases  with  distance,  I  have  not  been  able  to  deter- 
mine with  certainty.     It  is  probably  constant. 

2.  In  depressing  the  visual  plane,  the  inclination  of 
the  horopteric  line  becomes  less  and  less,  until  when 
the  visual  plane  is  inclined  45°  below  the  primary  posi- 
tion the  horopteric  line  becomes  perpendicular  to  the 
visual  plane,  and  at  the  same  time  expands  into  a  sur- 
face.    The  exact  nature  of  that  surface  I  have  not  at- 
tempted to  investigate,  for  reasons  already  explained ; 
but  it  is  evidently  a  curved  surface. 

3.  In  elevating  the  visual  plane,  especially  with 
strong  convergence,  the  inclination  of  the  horopteric 
line  increases. 

Finally,  the  question  naturally  occurs :  Of  what  ad- 
vantage is  this  outward  rotation  of  the  eyes,  and  the 
consequent  limitation  of  the  horopter  to  a  line  ?  Or  is 
it  not  rather  a  defect  ?  Should  the  law  of  Listing  be  re- 
garded as  the  ideal  of  ocular  motion  under  all  circum- 
stances, and  should  the  departure  from  this  law  in  the 


212  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

case  of  convergence  be  regarded  as  abnormal  ?  Or  is 
there  some  useful  purpose  subserved  by  the  rotation  of 
the  eyes  on  their  optic  axes?  I  feel  quite  sure  that 
there  is  a  useful  purpose  subserved ;  for  there  are  spe- 
cial muscles  adapted  to  produce  this  rotation,  and  the 
action  of  these  muscles  is  consensual  with  the  adjust- 
ments, axial  and  focal,  and  with  the  contraction  of  the 
pupil.  This  purpose  I  explain  as  follows : 

A  general  view  of  objects  in  a  wide  field  is  a  neces- 
sary condition  of  animal  life  in  its  higher  phases ;  but 
an  equal  distinctness  of  all  objects  in  this  field  would 
be  fatal  to  that  thoughtful  attention  which  is  necessary 
to  the  development  of  the  higher  faculties  of  the  human 
mind.  Therefore  the  human  eye  is  so  constructed  and 
moved  as  to  restrict  as  much  as  possible  the  conditions 
both  of  distinct  vision  and  of  single  vision.  Thus,  as 
in  monocular  vision  the  more  elaborate  structure  of  the 
central  spot  restricts  distinct  vision  to  the  visual  line, 
and  focal  adjustment  still  further  restricts  it  to  a  single 
point  in  that  line,  the  point  of  sight,  so  also  in  'binocu- 
lar vision  axial  adjustment  restricts  single  vision  to  the 
horopter,  while  rotation  on  the  optic  axes  restricts  the 
horopter  to  a  single  line. 


CHAPTER  III. 

ON  SOME  FUNDAMENTAL  PHENOMENA  OF  BINOCULAR 
VISION  USUALLY  OVERLOOKED,  AND  ON  A  NEW 
MODE  OF  DIAGRAMMATIC  REPRESENTATION  FOUND- 
ED THEREON. 

IN  all  that  I  have  said  thus  far,  I  have  made  use  of 
the  ordinary  mode  of  representing  binocular  visual  phe- 
nomena.    I  have  done  so  because  I 
could  thus  make  myself  more  easily 
understood.     But  it  is  evident  on  a 
little  reflection  that  the  usual  dia- 
grams do  not  in  any  case  represent 
the  real  visual  facts — i.  e.,  the  facts 
as  they  really  seem  to  the  binocular 
observer. 

Thus,  for  example,  if  a,  B,  and 
c,  Fig.  75,  be  three  objects  in  the 
median  plane,  but  at  different  dis- 
tances, and  the  two  eyes,  R  and  j£, 
be  converged  on  B,  as  already  ex- 
plained, a  and  c  will  be  both  seen 
double — the  former  heteronymous- 
ly,  the  latter  homonymously.  It 
will  be  observed  that  in  the  dia- 
gram the  double  images  of  both  a  and  c  are  referred  to 
the  plane  of  sight  P  P.  Now  every  one  who  has  ever 
tried  the  experiment  knows  that  the  double  images  are 
not  thus  referred  in  natural  vision ;  but,  on  the  con- 


214          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

trarj,  they  are  seen  at  their  real  distance,  though  not  in 
their  natural  position.  Indeed,  it  is  only  by  virtue  of  this 
fact  that  we  have  perception  of  binocular  perspective. 
The  diagram  therefore,  although  it  truly  represents  the 
parallactic  position  of  the  double  images,  does  not  rep- 
resent truly  their  apparent  distance.  If,  on  the  other 
hand,  we  attempt  in  the  diagram  to  refer  the  double 
images  to  their  real  distance  (observing  the  law  of  di- 
rection), then  they  unite  and  form  one,  which  is  equally 
untrue.  Thus,  if  we  represent  truly  the  visual  position, 
we  misrepresent  the  visual  distance ;  if,  on  the  con- 
trary, we  try  to  represent  the  visual  distance,  we  mis- 
represent the  visual  position.  It  is  evident  therefore 
that  the  usual  diagrams,  while  they  represent  truly 
many  important  visual  phenomena,  wholly  fail  to  rep- 
resent truly  many  others,  especially  the  facts  of  bin- 
ocular perspective. 

The  falseness  of  the  usual  mode  of  representation 
becomes  much  more  conspicuous  if,  instead  of  two  or 
more  objects,  we  substitute  a  continuous  rod  or  line. 
In  this  case  the  absurdity  of  projecting  the  double  im- 
ages on  the  plane  of  sight  is  so  evident  that  it  is  never 
attempted.  The  mode  universally  used  for  represent- 
ing the  visual  result  when  a  rod  is  placed  in  the  median 
plane  is  shown  in  Figs.  76-79,  of  which  Fig.  76  repre- 
sents the  actual  position  of  the  rod  in  the  median  plane, 
and  the  actual  position  of  the  visual  lines  when  the  eyes 
are  fixed  on  the  nearer  end  A  /  Fig.  77,  the  same  when 
the  eyes  are  fixed  on  the  farther  end  B  j  and  Figs.  78 
and  79,  the  visual  results  in  the  two  cases  respectively. 
Now  it  will  be  observed  that  in  both  these  figures  rep- 
resenting visual  results  (Figs.  78  and  79)  the  image  of 
the  rod  belonging  to  each  eye  is  coincident  with  the 
visual  line  of  the  other  eye,  and  therefore  makes  an 


ON  SOME  FUNDAMENTAL  PHENOMENA. 


215 


angle  with  its  own  visual  line  equal  to  the  visual  angle 
E  A  Z,  R  B  L.  But  this  is  not  true,  for  Figs.  76  and 
77  show  that  it  ought  to  make  but  half  that  angle.  If 


these  figures  therefore  truly  represent  the  position  of 
the  double  images  (as  indeed  they  do),  then  they  do 
not  represent  the  visual  or  apparent  position  of  the 
visual  lines.  The  truth  is,  in  natural  vision  the  visual 
10 


216  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

lines  are  shifted,  as  well  as  the  images  of  all  objects  not 
situated  at  the  point  of  sight,  and  to  the  same  degree, 
so  that  the  position  of  such  objects  relative  to  the  visual 
lines  is  perfectly  maintained  in  the  visual  result. 

It  is  evident  then  that  figures  constructed  on  the 
usual  plan,  while  they  give  correctly  the  place  and  dis- 
tance of  objects  seen  single,  fail  utterly  to  .  give  the 
place  of  double  images.  They  are  well  adapted  to 
express  binocular  combination  of  similar  objects  or 
similar  figures  on  the  plane  of  sight,  but  are  wholly 
inadequate  to  the  expression  of  the  facts  of  binocular 
perspective,  whether  in  natural  objects  or  scenes  or  in 
stereoscopic  pictures. 

In  an  article  published  in  January,  1871,*  I  pro- 
posed, therefore,  a  new  and  I  am  convinced  a  far  truer 
mode  of  diagrammatic  representation  of  the  phenomena 
of  binocular  vision,  applicable  alike  to  all  cases.  I  am 
satisfied  that  if  this  method  had  always  been  used,  much 
of  the  confusion  and  many  of  the  mistakes  to  be  found 
in  the  writings  on  binocular  vision  would  have  been 
avoided.  But  it  is  evident  that  such  a  new  and  truer 
method  must  be  founded  upon  some  fundamental  bin- 
ocular phenomena  usually  overlooked.  I  must  first 
therefore  enforce  these.  They  may  be  compendiously 
stated  in  the  form  of  two  fundamental  laws.  It  will 
be  best,  however,  before  formulating  them,  to  give  some 
familiar  experiments,  and  then  to  give  the  laws  as  an 
induction  from  the  facts  thus  brought  out. 

Experiment  1. — If  a  single  object,  as  for  example  & 
finger,  be  held  before  the  eyes  in  the  median  plane,  and 
the  eyes  be  directed  to  a  distant  point  so  that  their  axes 
are  parallel,  the  object  will  of  course  be  seen  double, 
the  heteronymous  images  being  separated  from  each 

*  "American  Journal  of  Science,"  Series  III,  vol.  i,  p.  33. 


ON  SOME  FUNDAMENTAL  PHENOMENA.  217 

other  by  a  space  exactly  equal  to  the  interocular  space. 
Now,  the  nose  is  no  exception  to  this  law.  The  nose  is 
always  seen  double  and  bounding  the  common  field  of 
view  on  either  side. 

Experiment  2. — If  two  similar  objects  be  placed 
before  the  eyes  in  the  horizontal  plane  of  sight,  and 
separated  by  a  space  exactly  equal  to  the  interocular 
space,  and  the  eyes  be  directed  to  a  distant  point  so  that 
their  axes  are  parallel  and  the  two  visual  lines  shall 
pass  through  the  two  objects,  then  both  objects  will  be 
doubled,  the  double  images  of  each  being  separated 
by  an  interocular  space ;  and  therefore  two  of  the  four 
images — viz.,  the  right-eye  image  of  the  right  object, 
and  the  left-eye  image  of  the  left  object — will  combine 
to  form  a  single  binocular  image  in  the  middle  /  while 
the  right-eye  image  of  the  left  object  will  be  seen  to 
the  left,  and  the  left-eye  image  of  the  right  object  to 
the  right.  Thus  there  will  be  three  images  seen — a 
middle  binocular  image,  and  two  monocular  images, 
one  on  each  side,  that  on  the  right  side  belonging  to 
the  left  eye  alone,  and  that  on  the  left  to  the  right 
eye  alone.  Now,  the  eyes  themselves  are  no  exception  to 
this  law.  In  binocular  vision  the  eyes  themselves  seem 
each  to  double — two  of  the  images  combining  to  form 
a  binocular  eye  in  the  middle  (ceil  cyclopienne),  while 
the  other  two  are  beyond  the  two  images  of  the  nose 
on  either  side.  Each  eye  seems  to  itself  to  occupy  a 
central  position,  while  it  sees  (or  would  see  if  the  nose 
were  not  in  the  way)  its  fellow  on  the  other  side  of  the 
double  images  of  the  nose. 

In  other  words,  in  binocular  vision,  when  the  optic 
axes  are  parallel,  as  in  gazing  on  a  distant  object,  the 
whole  field  of  view,  with  all  its  objects,  including  the 
parts  of  the  face,  is  shifted  by  the  right  eye  a  half  inter- 


218  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

ocular  space  to  the  left,  and  by  the  left  eye  a  half  inter- 
ocular  space  to  the  right,  without  altering  the  relative 
position  of  parts.  It  is  evident  that,  by  this  shifting  in 
opposite  directions,  the  two  eyes  with  their  visual  lines 
are  brought  together  in  perfect  coincidence,  so  that  cor- 
responding points  in  the  two  retinas  seem  to  be  perfectly 
united. 

FIG.  80.  FIG.  81. 


The  facts  as  thus  far  stated — both  the  actual  condi- 
tion of  things  as  we  know  them,  and  the  visual  results 
as  they  seem,  to  the  binocular  observer — are  represented 
in  the  following  diagrams.  Fig.  80  shows  the  actual 
condition  of  things,  and  Fig.  81  the  visual  result,  in  the 
first  experiment ;  Fig.  82  the  actual  condition  of  things, 
and  Fig.  83  the  binocular  visual  result,  in  the  second 
experiment.  To  explain  further :  In  Fig.  80,  7?  and  L 
are  the  right  and  left  eyes ;  N>  the  nose ;  A,  the  object 


ON  SOME  FUNDAMENTAL  PHENOMENA. 


219 


in  the  median  plane ;  the  dotted  lines  v  v,  the  direction 
of  the  visual  lines.  Fig.  81  represents  the  visual  results ; 
E  being  the  combined  or  binocular  eve  (mil  cyclopi- 
enne) ;  n  and  n',  the  two  images  of  the  nose  belonging 
to  the  right  and  left  eyes  respectively ;  F",  the  combined 
or  binocular  visual  line,  looking  between  the  double  im- 
ages a  and  a!  of  the  object  A;  while  rf  is  the  position 


FIG.  82. 


FIG.  83. 


of  the  right  eye  as  it  would  be  seen  by  the  left  eye,  and 
I  of  the  left  eye  as  it  would  be  seen  by  the  right,  if  the 
nose  were  not  in  the  way,  and  v  and  v'  are  the  positions 
of  their  visual  lines  if  they  were  visible  lines.  Fig.  82 
represents  the  actual  condition  of  things  when  two  sim- 
ilar objects  A  and  B  are  before  the  eyes  in  the  visual 
lines  v  v  •  and  Fig.  83  is  the  visual  result,  in  which  a! 
and  5  are  the  monocular  images,  one  belonging  to  the 
left  and  the  other  to  the  right  eye,  AE  the  combined 


220          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

or  binocular  image,  and  the  other  letters  representing 
the  same  as  before. 

Experiment  3. — These  facts  are  brought  out  still 
more  clearly  if,  instead  of  an  object  like  ^i,  Fig.  80,  we 
use  a  continuous  line  or  rod,  as  in  Fig.  76.  We  have 
seen  above  that,  with  the  optic  axes  parallel,  any  object 
placed  in  the  median  line  of  sight,  at  whatever  distance, 
is  separated  into  two  images  an  interocular  space  apart. 

FIG.  84.  FIG.  85. 


Evidently,  therefore,  the  median  line  of  sight  itself  is 
doubled,  and  becomes  two  lines,  which,  resting  on  the 
nose  on  each  side,  run  out  parallel  to  each  other  indefi- 
nitely. Between  these  two  lines  the  binocular  eye 
(combined  eyes)  looks  out  along  the  combined  visual 
line  at  a  distant  object.  If  the  median  line  be  occu- 
pied by  a  real  visible  line  or  a  rod,  we  shall  see  two 
parallel  lines  or  rods.  If  the  median  plane  be  occu- 


ON  SOME  FUNDAMENTAL  PHENOMENA.  221 

pied  by  a  real  plane,  we  shall  see  two  parallel  planes 
bounding  the  binocular  field  of  view  on  each  side,  be- 
tween which  we  look. 

These  facts  are  represented  by  the  diagrams  Figs. 
84  and  85.  In  Fig.  84,  B  represents  a  rod  resting  on 
the  root  of  the  nose  n,  and  held  in  place  by  the  point 
of  the  finger  A  ;  R  and  L  are  the  two  eyes,  and  v  and 
v  the  two  visual  lines  in  a  parallel  position.  Such  is 
the  actual  condition  of  things.  Now  Fig.  85  represents 
the  visual  results.  It  is  seen  that  the  nose  n,  the  rod  B, 
and  the  finger-point  A  of  fig.  84  are  all  doubled,  as  n  n', 
b  bf,  a  a!  of  fig.  85  ;  while  the  two  eyes,  R  and  Z,  and 
the  two  visual  lines,  v  and  v,  of  fig.  84,  are  combined  in 
the  middle  as  the  binocular  eye  E,  which  looks  out  along 
the  combined  visual  line  V  between  the  parallel  rods 
b  V,  of  fig  85. 

As  already  stated,  if  instead  of  a  rod  we  use  a  plane 
coincident  with  the  median  plane,  then  the  plane  is 
doubled,  and  we  look  between  the  doubled  images. 
This  is  the  case  in  using  the  stereoscope.  The  median 
plane  of  the  stereoscope  is  doubled,  and  between  its 
two  images  we  look  out  on  the  combined  pictures. 

Experiment  4- — An  excellent  illustration  of  the  fun- 
damental fact,  that  in  binocular  vision  the  two  eyes  are 
moved  to  the  middle  and  combined  into  a  binocular 
eye,  must  be  familiar  to  every  one  who  has  ever  worn 
spectacles.  If  the  spectacles  are  properly  chosen,  so 
that  the  distance  between  the  centers  of  the  two  glasses 
is  exactly  equal  to  the  interocular  space,  then  we  see 
but  on.e  glass  exactly  in  the  middle,  through  which  the 
binocular  eye  seems  to  look.  We  would  see  two  other 
glasses,  monocular  images,  right  and  left,  if  these  were 
not  hidden  by  the  nose.  We  do  indeed  see  two  others 
in  these  positions  if  we  remove  the  spectacles  to  such 


222  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

distance  that  the  nose  no  longer  conceals  them,  while  we 
still  look  through  the  middle  glass  at  a  distant  object. 

Many  other  familiar  illustrations  may  be  given.  If 
we,  put  our  face  against  a  mirror,  so  that  forehead  and 
nose  shall  touch  the  glass,  and  then  gaze  on  vacancy, 
there  will  be  of  course  four  images  of  the  two  eyes  in 
the  mirror.  Two  of  these,  viz.,  the  right-eye  image  of 
the  right  eye  and  the  left-eye  image  of  the  left  eye, 
will  unite  to  form  a  central  binocular  eye,  an  image  of 
our  own  central  binocular  eye,  and  into  which  our  own 
seems  to  gaze.  The  nose  will  be  seen  double  and  on 
each  side  of  the  central  eye,  and  beyond  the  double  im- 
ages of  the  nose  on  either  side  will  be  seen  monocular 
images  of  the  eyes.  In  other  words,  we  actually  see 
exactly  what  I  have  expressed  in  the  diagrams  (Figs. 
83  and  85)  representing  visual  results. 

If,  in  place  of  the  reflection  of  our  own  face  in  a 
mirror,  we  make  use  in  this  experiment  of  the  face  of 
another  person,  placing  forehead  against  forehead,  nose 
against  nose,  and  the  eyes  exactly  opposite  each  other, 
and  gaze  on  vacancy,  the  same  visual  result  will  follow. 
Our  own  central  binocular  eye  looks  between  our  two 
noses  into  another  central  binocular  eye,  situated  also 
between  two  noses.  Other  monocular  eyes  are  seen 
beyond  the  noses,  right  and  left. 

The  fields  of  view  of  the  two  eyes  are  bordered  by 
the  nose,  the  brows,  and  the  cheeks.  Its  form  there- 
fore varies  in  different  persons.  It  has  no  definite  limit 
on  the  outside.  I  reproduce  as  Fig.  86  the  diagram 
already  used  on  page  91,  representing  rudely  the  gen- 
eral character  of  the  field  of  view  of  the  binocular  ob- 
server. I  have  introduced  the  ceil  cydopienne  and  the 
two  monocular  images  of  the  eyes;  and,  in  order  to 
make  it  more  comprehensible,  I  have  supposed  the  ob- 


ON  SOME  FUNDAMENTAL  PHENOMENA.  223 

server  to  wear  glasses.  In  this  diagram,  n  n  is  an  out- 
line of  the  nose,  ~br  of  the  brow,  and  ch  of  the  cheek  of 
the  right- eye  field  ;  &/,  n'  n',  and  ch',  the  outline  of  the 
left-eye  field.  The  middle  space  where  they  overlap, 
bounded  on  each  side  by  the  outline  of  the  nose,  n  n, 
n'  n' ,  is  the  common  or  binocular  field  occupied  by  the 
central  binocular  eye  E,  surrounded  by  tke  single  ellipse 


FIG.  86. 


of  the  combined  spectacle-glasses.  I  have  also  intro- 
duced in  dotted  outline  the  left  eye  I  and  the  spectacle- 
rim  s  s  as  they  would  be  seen  by  the  right  eye,  and  the 
right  eye  r'  and  spectacle-rim  s'  s'  as  they  would  be 
seen  by  the  left  eye,  if  the  nose  were  not  in  the  way. 

First  Law. — We  are  now  in  position  to  formulate 
the  first  law.  I  would  express  it  thus:  In  binocular 
vision,  with  the  optic  axes  parallel,  as  in  looking  at  a 
distant  object,  the  whole  field  of  view  and  all  objects 
in  the  field,  including  the  visible  parts  of  the  face,  are 
shifted  by  the  right  eye  a  half  interocular  space  to  the 
left,  and  by  the  left  eye  the  same  distance  to  the  right, 
without  altering  the  relative  positions  of  parts ;  so  that 
the  two  eyes  with  their  two  visual  lines  seem  to  unite 
to  form  a  single  middle  binocular  eye,  and  a  single 


224          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

middle  visual  line,  along  which  the  eye  seems  to  look. 
It  follows  that  any  line,  rod,  or  plane  in  the  median 
line,  as  also  the  nose  itself,  is  doubled  heteronymously, 
and  becomes  two  lines,  rods,  or  planes,  parallel  to  each 
other,  and  separated  by  a  space  exactly  equal  to  the 
interocular  space.  Between  the  two  noses,  and  between 
the  two  parallel  lines,  rods,  or  planes,  the  binocular  eye 
seems  to  look  out  along  the  middle  visual  line  upon  the 
distant  object.  Of  course,  by  this  shifting  of  the  two 
fields  in  opposite  directions,  all  objects  in  the  field  are 
similarly  doubled. 

Thus  in  binocular  vision  the  two  eyes  seem  actually 
to  be  brought  together  and  superposed,  and  correspond- 
ing points  of  the  two  retinae  to  coincide.  The  two  eyes 
become  actually  one  instrument.  And  conversely,  this 
apparent  combination  of  two  eyes  and  their  visual  lines 
is  a  necessary  consequence  of  the  law  of  corresponding 
points.  For  images  on  corresponding  points  are  seen 
single ;  all  objects  on  the  two  visual  lines  must  impress 
corresponding  points,  viz.,  the  central  spots ;  therefore 
the  visual  lines  themselves,  if  they  were  visible  lines, 
would  be  seen  single.  But  where  could  they  be  seen 
single  except  in  the  middle  ?  Therefore  the  two  visual 
lines  must  combine  to  form  a  single  middle  visual  line. 

We  will  next  give  experiments  leading  up  to  the 
second  law.  For  this  purpose  let  us  recur  to  the  ex- 
periment with  the  rod  represented  by  Fig.  84.  We 
reproduce  this  as  Fig.  87,  in  order  to  compare  with  it 
the  results  of  subsequent  experiments.  As  already  ex- 
plained, if  the  rod  B  be  placed  in  the  median  plane 
with  the  nearer  end  resting  on  the  nose-root  n,  and  the 
farther  end  held  in  place  by  the  point  of  the  finger  A, 
the  eyes  looking  at  a  distant  object,  as  shown  in  Fig. 
87,  which  represents  the  actual  condition  of  things,  then 


ON  SOME  FUNDAMENTAL  PHENOMENA. 

FIG.  87.  FIG.  88. 


225 


the  rod,  together  with  nose  and  finger-point,  will  be 
doubled  heteronymously  and  become  two  parallel  rods, 


FIG.  89. 


Fro.  90. 


226  DISPUTED   POINTS  IN   BINOCULAR  VISION. 

between  which,  the  binocular  eye  will  look  out  along 
the  binocular  visual  line  at  the  distant  object,  as  shown 
in  Fig.  88,  which  represents  the  visual  result. 

Experiment  1. — Now,  while  we  hold  the  rod  in  the 
position  represented  by  Fig.  87,  instead  of  looking  at  a 
distant  object  with  eyes  parallel,  let  the  eyes  be  con- 
verged on  the  finger-point  F,  so  that  Fig.  89  shall  rep- 
resent the  actual  condition  of  things.  We  will  observe 
that  the  double  images  of  the  rod  represented  in  the 
visual  result,  Fig.  88,  approach  at  their  farther  end,  car- 

Fio.  91.  FIG.  92. 


rying  all  objects  in  the  field  with  them,  until  they  unite 
at  the  point  of  sight  F^  and  we  have  the  visual  result 
represented  in  Fig.  90. 

Experiment  2. — If  by  greater  convergence  we  next 
look  at  some  nearer  point  B  on  the  rod,  as  in  Fig.  91, 
which  represents  the  actual  relation  of  parts,  then  Fig. 
92  represents  the  visual  result.  By  comparing  this  with 


ON  SOME  FUNDAMENTAL  PHENOMENA.  227 

the  previous  visual  results,  Figs.  88  and  90,  it  will  be 
seen  that  the  double  images  5  V  approach  each  other 
until  they  unite  at  the  point  of  sight,  and  the  two  im- 
ages of  the  rod  cross  each  other  at  this  point,  and  there- 
fore become  again  double  beyond,  but  now  homony- 
rnously.  If  by  still  greater  convergence  we  look  at  a 
still  nearer  point  C\  Fig.  93,  then  the  double  images 
of  the  median  rod,  Figs.  87,  89,  91,  will  cross  at  the  point 
of  sight  (7,  and  give  the  visual  result  shown  in  Fig.  94. 

FIG.  93.  FIG.  94. 


Finally,  if  the  point  of  sight  by  extreme  convergence 
be  brought  to  the  root  of  the  nose,  then  the  double  im- 
ages of  the  nose  n  nr,  Figs.  92,  94,  will  be  brought  in  con- 
tact, and  the  common  or  binocular  field  will  be  obliter- 
ated. In  all  cases  it  will  be  observed  that  the  combined 
eyes  look  along  the  combined  visual  lines  through  the 
point  of  sight,  and  onward  to  infinite  distance. 

It  is  evident,  then,  that  in  optic  convergence,  as  the 
two  real  eyes  turn  in  opposite  directions  on  their  optic 


228          DISPUTED  POINTS  IX  BINOCULAR  VISION. 

centers,  the  two  fields  of  view  turn  also  on  the  center 
of  the  binocular  eye  in  directions  opposite  to  the  real 
eyes,  and  therefore  to  each  other. 

It  will  be  observed  that  in  speaking  of  visual  phe- 
nomena I  have  used  much  the  same  language  as  other 
writers  on  this  subject,  and  used  also  a  somewhat  simi- 
lar mode  of  representation  ;  only  I  have  substituted  eyes 
in  the  place  of  the  nose,  and  put  noses  in  the  position 
of  the  eyes.  I  have  made  median  lines  cross  each  other 
at  the  point  of  sight,  instead  of  visual  lines,  and  visual 
lines  combine  in  the  middle  as  a  true  median  visual 
line.  In  other  words,  I  have  used  the  true  language 
of  binocular  vision.  I  have  expressed  what  we  see, 
rather  than  what  we  know — the  language  of  simple 
appearance,  rather  than  that  mixture  of  appearance  and 
reality  which  forms  the  usual  language  of  writers  on 
this  subject. 

Second  Law. — The  second  law  may  therefore  be 
stated  thus :  In  turning  the  eyes  in  different  directions 
without  altering  their  convergence,  objects  seem  sta- 
tionary, and  the  visual  lines  seem  to  move  and  sweep 
over  them ;  but  when  we  turn  the  eyes  in  opposite 
directions,  as  in  increasing  or  decreasing  their  conver- 
gence, then  the  visual  lines  seem  stationary  (i.  e.,  we 
seem  to  look  in  the  same  direction  straight  forward), 
and  all  objects,  or  rather  their  images,  seem  to  move 
in  directions  contrary  to  the  actual  motion  of  the  eyes. 
The  whole  fields  of  view  of  both  eyes  seem  to  rotate 
about  a  middle  optic  center,  in  a  direction  contrary  to 
the  motion  of  the  corresponding  eyes,  and  therefore  to 
each  other.  This  is  plainly  seen  by  voluntarily  and 
strongly  converging  the  eyes  on  an  imaginary  very  near 
point,  as  for  example  the  root  of  the  nose,  and  at  the 
same  time  watching  the  motion  of  the  images  of  more 


ON  SOME  FUNDAMENTAL  PHENOMENA.  229 

distant  objects.  The  whole  field  of  view  of  the  right 
eye,  carrying  all  its  images  with  it,  seems  to  rotate  to 
the  right,  and  of  the  left  eye  to  the  left — i.  e.,  homony- 
mously.  The  images  of  all  objects,  as  they  are  swept 
successively  by  the  two  visual  lines,  are  brought  from 
opposite  directions  to  the  front  and  superposed.  As 
we  relax  the  convergence,  and  the  eyes  move  back  to 
a  parallel  condition,  the  two  fields  with  their  images 
are  seen  to  rotate  in  the  other  direction — i.  e,  heterony- 
mously.  If  we  could  turn  the  eyes  outward,  the  two 
fields  and  their  images  would  continue  to  rotate  het- 
eronymously.  This,  which  we  can  not  do  by  volun- 
tary effort  of  the  ocular  muscles,  may  be  done  by 
pressing  the  fingers  in  the  external  corners  of  the  two 
eyes.  By  pressing  in  the  internal  corners,  on  the  con- 
trary, the  eyes  are  made  to  converge,  and  homonymous 
rotation  of  the  fields  of  view  is  produced. 

Or  the  law  may  be  more  briefly  formulated  thus : 
In  convergence  and  divergence  of  the  eyes,  the  two 
fields  of  view  rotate  in  opposite  directions,  hornony- 
mously  in  the  former  case  and  heteronymously  in  the 
latter,  about  the  optic  center  of  the  binocular  eye  (mil 
cyclopienne),  while  the  middle  or  binocular  visual  line 
maintains  always  its  position  in  the  median  plane. 

Thus,  then,  there  are  two  apparent  movements  of 
the  visual  fields  accomplished  in  binocular  vision.  First, 
there  is  a  shifting  of  each  field  heteronymously  a  half 
interocular  space.  This  is  involuntary  and  habitual, 
and  would  of  itself  double  all  objects  heteronymously, 
separating  their  images  exactly  an  interocular  space. 
Second,  in  convergence,  there  is  a  rotation  of  each  field 
about  the  optic  center  of  the  ceil  cyclopienne  (or  about 
an  axis  passing  through  that  center  and  normal  to  the 
visual  plane),  homonymously.  The  necessary  conse- 


230          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

quences  of  these  movements  are :  (a)  that  the  images 
of  an  object  at  the  point  of  sight  are  superposed  and 
the  object  is  seen  single,  while  objects  on  this  side  of 
the  point  of  sight  are  doubled  heteronymously,  and 
those  beyond  the  point  of  sight  homonymously ;  (&) 
that  all  objects  (different  objects)  lying  in  the  direction 
of  the  two  visual  lines,  whether  nearer  than  or  beyond 
the  point  of  sight,  have  their  images  (one  of  each) 
brought  to  the  front  and  superposed ;  so  that  the  two 
visual  lines  are  under  all  circumstances  brought  together 
and  combined  to  form  a  single  binocular  visual  line, 
passing  from  the  middle  binocular  eye  through  the 
point  of  sight  and  onward  to  infinity. 

In  all  the  experiments  which  follow  on  this  subject 
it  is  necessary  to  get  the  interocular  space  with  exact- 
ness. This  may  be  done  very  easily  in  the  following 
manner : 

Experiment. — Take  a  pair  of  dividers  and  hold  it 
at  arm's  length  against  the  sky  or  a  bright  cloud,  and, 
while  gazing  steadily  at  the  sky  or 
cloud,  separate  the  points  until  two 
of  the  four  double  images  of  the 
points  shall  unite  perfectly,  as  in 
Fig.  95.  The  distance  between 
the  points  of  the  dividers,  equal  to 
a-a',  or  #-&',  or  c-e',  is  exactly  the 
interocular  distance — i.  e.,  the  dis- 
tance between  the  central  points 
of  the  central  spots  of  the  two 
retinoe.  The  only  difficulty  in  the  way  of  perfect  ex- 
actness in  this  experiment  is  the  want  of  fine  definition 
of  the  points  when  the  eyes  are  adjusted  for  distant 
vision.  This  may  be  obviated  by  using  slightly  convex 
spectacles.  The  accuracy  of  the  determination  may  be 


ON  SOME  FUNDAMENTAL  PHENOMENA.  231 

verified  thus :  Measure  the  distance  just  determined  ac- 
curately on  a  card,  and  pierce  the  card  at  the  two  points 
with  small  pin-holes.  Now  place  the  card  against  the 
forehead  and  nose,  with  the  holes  exactly  in  front  of 
the  two  eyes,  and  gaze  through  them  at  a  distant  hori- 
zon or  cloud.  If  the  measurement  is  exact,  the  two 
pin-holes  will  appear  as  one ;  their  coincidence  will  be 
perfect.  As  thus  determined,  I  find  my  interocular 
space  almost  exactly  2£  inches  (63.5  mm.).  It  will  be 
seen  that  this  method  is  founded  upon  the  opposite 
shifting  of  the  two  fields  of  view  half  an  interocular 
space  each,  spoken  of  in  the  first  law.  The  two  pin- 
holes  are  seen  as  one  exactly  in  the  middle,  which  is 
looked  through  by  the  ml  cydopienne  •  and  this  is 
therefore  one  of  the  very  best 
illustrations  of  such  shifting 
of  the  two  eyes  and  their  vis- 
ual lines  to  the  middle. 

We  will  now  give  some  ad- 
ditional experiments  illustrat- 
ing and  enforcing  these  two 
laws,  and  showing  the  absolute 
necessity  of  using  this  new 
mode  of  diagrammatic  repre- 
sentation in  all  cases  in  which 
binocular  perspective  is  in- 
volved. For  this  purpose  I 
find  it  most  convenient  to  use 
a  small  rectangular  blackboard 
about  18  inches  long  and  10 
inches  wide,  Fig.  96.  Mark 

two  points  R  and  L  at  one  end,  with  a  space  between 
exactly  equal  to  the  interocular  space,  and  in  the  middle 
between  these  points  make  a  notch  n  in  the  edge  of  the 


232          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

board  to  fit  over  the  bridge  of  the  nose.  Such  a  board 
is  admirably  fitted  for  all  experiments  on  binocular  per- 
spective. 

Experiment  1. — Draw  a  line  through  the  middle  of 
the  board  from  the  notch  n,  Fig.  96.  This  will  be  the 
visible  representative  of  the  median  line ;  and  as  the 
median  line  is  used  in  all  the  experiments,  this  may  be 
made  permanent.  On  this  line  place  two  pins. at  A  and 
B.  Draw  also  from  the  points  L  and  R  dotted  lines 

FIG.  97.  FIG.  98. 


parallel  to  the  median  line  and  to  each  other,  as  the 
visible  representatives  of  the  visual  lines  when  the  optic 
axes  are  parallel,  as  when  looking  at  a  distant  object. 
Now  fit  the  plane  over  the  bridge  of  the  nose,  and 
place  it  in  a  horizontal  position  a  little  below  the  pri- 
mary plane  of  vision,  say  half  an  inch  or  an  inch,  so 
that  the  whole  surface  is  distinctly  seen,  and  then  look 


OX  SOME  FUNDAMENTAL  PHENOMENA.  233 

beyond  at  a  distant  object.  Leaving  out  the  board  in 
the  representations,  the  actual  position  of  the  lines  is 
shown  in  Fig.  97  and  the  visual  result  in  Fig.  98.  Re- 
membering that  in  all  our  figures  capitals  represent 
combined  or  binocular  images,  simple  italics  right-eye 
images,  and  primed  italics  left-eye  images,  it  will  be 
seen  that  the  whole  board,  with  all  the  lines  and  objects 
on  it  and  the  parts  of  the  face,  has  been  shifted  left 
and  right  by  the  two  eyes,  so  that  the  nose  and  the 
median  line  are  seen  as  two  noses  and  two  parallel  lines 
with  their  pins,  separated  by  a  space  exactly  equal  to 
the  interocular  space,  and  the  two  visual  lines  are 
brought  together  and  united  in  the  middle  to  form  a 
common  visual  line  Fi  as  if  coming  from  a  single  bin- 
ocular eye  K  If  two  small  circles  be  drawn  or  a  pin 
be  set  at  the  end  of  the  dotted  visual  lines  in  Fig.  97, 
these  will  be  united  in  the  result  Fig.  98,  at  the  end  of 
the  combined  visual  line  V.  There  will  also  of  course 
be  seen  to  the  extreme  right  and  left  monocular  images 
of  the  dotted  representatives  of  the  visual  lines,  and  of 
the  circles  or  pins  at  their  farther  end.  I  have  con- 
nected by  vincula  the  images  of  the  whole  drawing, 
the  primed  vinculum  being  the  image  of  the  left  eye, 
the  other  of  the  right. 

Experiment  *2. — If  we  now  erase  the  parallel  visual 
lines  v  v  on  the  board,  and  draw  them  convergent  on 
the  pin  A,  so  that  Fig.  99  shall  represent  the  actual 
condition,  and  then  adjust  the  board  again  to  the  nose 
and  look  at  the  pin  A,  the  visual  result,  or  what  we  shall 
see,  is  given  in  Fig.  100.  By  comparing  this  result  with 
the  actual  condition  of  things — i.  e.,  by  comparing  Fig. 
100  with  Fig.  99 — it  would  seem  as  if  the  whole  draw- 
ing on  the  board,  including  the  eyes  and  nose,  had  been 
turned  about  the  point  of  sight  A  by  the  two  eyes  in 


234:  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

opposite  directions,  the  right  carrying  it  to  the  position 
I  A  E,  the  left  eye  to  the  position  r'  A  E,  shown  by 
the  unprimed  and  the  primed  vinculum  respectively. 


FIG.  99.  FIG.  100. 


The  real  nature  of  the  rotation,  however,  is  shown  by 
comparing  the  appearance  of  the  drawing  when  the 
eyes  are  parallel  with  its  appearance  when  the  eyes  are 
converged  on  A.  Fig.  101  represents  the  visual  result 
when  the  same  drawing  is  viewed  with  the  eyes  par- 
allel. By  comparing  this  figure  with  the  visual  result 
when  the  eyes  converge  on  A  (Fig.  100),  it  is  seen  that 
the  two  images  of  the  whole  drawing  rotate  on  the 
optic  center  of  the  binocular  eye  E,  until  the  pins  a  a' 
and  the  visual  lines  v  v'  of  Fig.  101  unite  to  form  the 
binocular  image  A  and  the  binocular  visual  line  V  of 
Fig.  100.  If  the  eyes  be  converged  very  gradually, 
the  slow  approach  of  the  points  a  a!,  carrying  with  them 
the  dotted  lines  v  v',  as  if  turning  on  the  center  of  the 
binocular  eye  E,  can  be  distinctly  seen. 


ON  SOME  FUNDAMENTAL   PHENOMENA.  235 

Experiment  3. — If  we  again  erase  the  dotted  repre- 
sentatives of  the  visual  lines  and  draw  them  converging 
and  crossing  at  the  nearer  pin  B, 
as  in  Fig.  102,  then  Fig.  103  gives 
the  visual  result.  It  is  as  if  the 
whole  diagram,  Fig.  102,  had  been 
rotated  on  the  point  of  sight  B  in 
two  directions,  viz.,  a  right-handed 
rotation  by  the  right  eye  and  a 
left-handed  rotation  by  the  left 
eye.  But  what  actually  takes 
place  is  seen  by  first  gazing  at  a 
distant  object  and  comparing  the 
visual  result  thus  obtained,  shown 
in  Fig.  104,  with  that  obtained  by 
converging  the  eyes  on  B,  shown 
in  Fig.  103.  It  is  seen  that  the 
double  images  of  the  whole  dia- 
gram turn  on  the  center  E  until  b  fr ',  Fig.  104,  unite  to 
form  B,  Fig.  103,  and  v  E,  vf  Eto  form  V  E;  and  of 
course  the  other  lines,  a  a' ',  v  v',  cross  over  and  become 
homonymous.  When  the  eyes  converge  as  in  this  last 
experiment,  the  points  It  and  L  on  the  experimental 
board,  Fig.  98,  must  be  a  little  less  than  an  interocular 
space  apart. 

Let  us  now  return  to  the  original  experiment  with 
three  points  or  objects  in  the  median  line  given  on  page 
213.  We  reproduce  here  the  figure  (Fig.  105)  usually 
used  to  illustrate  the  visual  result.  We  have  already 
shown  how  impossible  it  is  to  represent  all  the  visual 
results  in  this  way.  If  we  are  bent  on  representing  the 
parallactic  position  of  the  double  images,  then  we  must 
refer  them  all  to  the  same  plane,  as  in  Fig.  105 ;  but 
this  is  false.  If,  on  the  other  hand,  we  try  to  place 


236          DISPUTED  POINTS  IN  BINOCULAR  VISION. 
FIG.  102.  FIG.  103. 


them  at  the  distances  at  which  we  actually  see  them, 
observing  the  law  of  direction,  then  the  double  images 
unite,  which  is  also  false. 

FIG.  104.  PIG.  105. 


ON  SOME  FUNDAMENTAL  PHENOMENA.  237 

Experiment  4- — Now  try  the  same  experiment  by 
the  use  of  the  board,  and  the  true  mode  of  representa- 
tion becomes  manifest.  On  the  median  line,  Fig.  106, 
place  three  pins,  and  draw  dotted  lines  to  each  of  them 
from  the  position  of  the  eyes,  which  shall  be  the  vis- 
ible representatives  of  either  visual  lines  or  ray-lines. 
As  in  the  experiment  the  eyes  will  look  at  J?,  let  the 
dotted  lines  to  E  be  stronger  to  represent  visual  lines ; 

FIG.  106.  FIG.  10T. 


then  the  others  will  represent  only  ray-lines.  Now 
when  this  diagram  is  observed  with  the  point  of  sight 
at  B,  Fig.  106,  then  the  visual  result — i.  e.,  what  we 
actually  see  on  the  board — will  be  Fig.  107.  It  is  seen 
that  the  whole  diagram  Fig.  106  is  rotated  in  opposite 
directions  about  the  point  of  sight  B  to  make  the  result, 
Fig.  107.  But  the  real  nature  of  the  rotation  is  shown 
by  comparing  the  result  with  the  eyes  parallel,  Fig.  108, 
with  the  result  with  the  eyes  converged  on  B,  Fig.  1 07. 


238  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

"With  the  eyes  parallel,  the  whole  diagram  is  simply 
doubled  heteronymously  by  each  eye  shifting  it  half  an 
interocular  space  in  opposite  directions.     Now  conver- 
Fro  m  ging  the  eyes  slowly,  the  two 

images  of  Fig.  106  shown  in 
Fig.  108  are  seen  to  rotate  on 
E  until  the  points  b  V  and  the 
dotted  lines  b  E^  V  E  unite  to 
form  B  E,  Fig.  107.  In  do- 
ing so,  c  c'  have  approached, 
but  not  united ;  they  are  there- 
fore still  heteronymous,  while 
a  a!  have  met  and  passed  each 
other,  and  become  homony- 
mously  double. 

Therefore  Fig.  107  truly 
represents  all  the  visual  facts. 
It  gives  both  the  parallactic 
position  of  the  points  in  rela- 
tion to  the  observer,  their  relative  position  in  regard 
to  each  other,  and  their  relative  distance.  Or,  if  we 
leave  out  in  the  original  diagram,  as  complicating  the 
figure,  all  except  the  necessary  median  line  and  pins, 
as  in  Fig.  109,  then  the  visual  result  is  given  in  Fig. 
110.  Or,  adding  in  the  visual  result  only  the  visual 
line  and  the  most  necessary  ray-lines,  viz.,  those  going 
to  the  binocular  eye,  we  have  Fig.  111.  This  last  fig- 
ure we  shall  hereafter  use  to  represent  the  phenomena 
of  binocular  perspective. 

Application  to  Stereoscopic  Phenomena. — We  wish 
now  to  apply  this  new  method  of  representation  to  the 
phenomena  of  the  stereoscope.  We  reproduce  here  as 
Fig.  112  the  diagram  used  on  page  131.  It  is  seen  that 
while  the  different  distances,  A  and  B,  at  which  the 


ON  SOME  FUNDAMENTAL   PHENOMENA.  239 

foreground  and  background  are  seen,  are  truly  repre- 
sented, no  attempt  is  made  to  represent  the  double  im- 
ages of  the  foreground  when  the  background  is  re- 
garded, or  vice  versa.  It  is  impossible  by  this  usual 
method  to  represent  these  double  images  without  refer- 

FIG.  109.  FIG.  110.  FIG.  111. 


ring  them  to  the  same  plane ;  but  this  would  of  course 
destroy  the  perspective,  which  it  is  the  very  object  of 
the  diagram  to  illustrate.  The  new  method,  on  the 
contrary,  represents  the  true  distance  of  the  point  of 
sight,  and  the  true  positions  and  distances  of  the  double 
images,  and  therefore  the  true  binocular  perspective. 
In  other  words,  it  represents  truly  all  the  binocular 
visual  phenomena.  It  will  be  best  to  preface  this  ex- 
planation by  an  additional  experiment. 

Experiment. — If  a  rectangular  card,  like  an  ordinary 

stereoscopic  card,  or  a  letter  envelope,  be  held  before 

the  face  at  any  convenient  distance  while  the  eyes  gaze 

on  vacancy,  i.  e.,  with  the  optic  axes  parallel,  the  two 

11 


240 


DISPUTED   POINTS  IN  BINOCULAR  VISION. 


FIG.  112. 


images  of  the  card  will  be  seen  to  slide  over  each  other 
heteronymously,  each  a  distance  equal  to  a  half  inter- 
ocular  space,  and  therefore  relatively  to  each  other  ex- 
actly an  interocular  space.  If  the  card  be  longer  than 
an  interocular  space,  there  will  be  a 
part  where  the  two  images  will  overlap. 
This  is  represented  in  the  accom- 
panying diagrams,  of  which  Fig.  113 
represents  the  card  when  looked  at, 
and  Fig.  114  the  visual  result  when 
the  eyes  are  parallel.  In  this  visual 
result  c  c  is  the  right-eye  image  of 
the  card,  c'  c'  the  left-eye  image,  and 
d  d  the  binocular  overlapping.  This 
overlapped  part  will  be  opaque,  be- 
cause nothing  can  be  seen  behind  it 
by  either  eye.  But  right  and  left  of 
this  are  two  transparent  spaces.  That 
on  the  left  belongs  to  the  image  of  the 
right  eye,  but  not  to  that  of  the  left, 
and  therefore  the  left  eye  sees  objects 
beyond  it.  That  on  the  right  belongs 
to  the  left  eye,  but  the  right  eye  sees  objects  beyond  it. 
If  two  circles,  a  a,  be  drawn  on  the  card,  Fig.  113, 
an  interocular  space  apart,  they  wrill  unite  into  a  bin- 


FIG.  113. 


FIG.  114. 


a. 

o 


ft' 

o 


ocular  circle  A  in  the  center  of  the  opaque  part,  Fig. 
114;  while  two  monocular  circles  a  a!  will  occupy  the 
transparent  borders. 


ON  SOME   FUNDAMENTAL  PHENOMENA.  241 

By  the  law  of  alternation  spoken  of  on  page  93, 
sometimes  the  right  eye  will  prevail,  the  right-hand  trans- 
parent border  will  disappear,  and  the  whole  right-eye 
image  c  c  will  appear  opaque.  Then  the  left  eye  pre- 
vails, and  the  left-hand  border  will  disappear,  and  the 
whole  left-eye  image  c'  c'  will  appear  opaque.  Some- 
times both  borders  disappear,  and  only  the  binocular 
overlapping  is  seen.  Sometimes  the  whole  double  im- 
age, including  both  borders,  becomes  opaque.  But  the 
true  normal  binocular  appearance  or  visual  result  is 
given  in  Fig.  114 — i.  e.,  opaque  center  and  transparent 
borders,  these  borders  being  exactly  equal  to  the  inter- 
ocular  space. 

We  are  now  prepared  to  show  how  stereoscopic 
phenomena  may  be  represented  by  our  new  method. 
In  Fig.  115,  c  c  represents  a  stereoscopic  card  in  posi- 
tion ;  in  s,  the  median  screen,  which  cuts  off  the  super- 
numerary monocular  images ;  a  a,  identical  points  in 
the  foreground  of  the  pictures,  and  b  J,  in  the  back- 
ground. The  two  eyes  and  the  nose  are  represented 
as  before  by  It,  Z,  and  n  ;  and  a  7?,  a  L,  1>  7?,  b  L  are 
ray-lines.  Leaving  out  the  dotted  lines  beyond  the 
card,  this  diagram  represents  the  actual  condition  of 
things.  The  dotted  lines  beyond  the  picture  show  the 
mode  of  representation  usually  adopted.  When  the 
eyes  are  directed  to  a  a,  then  a  .7?,  a  L  become  visual 
lines,  and  a  a  are  united  and  seen  at  the  point  of  sight 
A.  When  the  eyes  are  directed  to  b  5,  then  b  7?,  b  L 
become  visual  lines,  and  b  and  b  are  united  and  seen 
single  at  the  point  of  sight  B. 

The  defect  of  this  mode  of  representation  is,  that  it 
takes  no  cognizance  of  the  double  images  of  b  b  when 
A  is  regarded,  or  of  a  a  when  B  is  regarded.  The  at- 
tempt to  represent  these  would  destroy  the  perspective. 


242 


DISPUTED  POINTS  IN  BINOCULAR  VISION. 


By  our  new  method,  on  the  contrary,  all  the  phe- 
nomena are  represented.  In  Fig.  116  is  shown  the 
visual  result  when  the  eyes  are  fixed  on  the  background  ; 
in  Fig.  117,  the  visual  result  when  the  eyes  are  fixed 


on  the  foreground.  In  Fig.  116  we  see  that  the  nose 
n  n'  and  the  median  screen  ms  m's  are  doubled  heter- 
onymously,  and  the  space  between  the  two  is  the  com- 
mon and  only  field  of  view  (for  the  monocular  fields 


ON  SOME  FUNDAMENTAL  PHENOMENA.  243 

are  cut  off  by  the  screen).  In  the  middle  between  these 
is  the  binocular  eye  E,  looking  straight  forward.  This 
is  manifestly  exactly  what  we  see  in  the  stereoscope. 
Again,  we  see  that  the  two  images  of  the  card  have 
slidden  over  each  other,  in  such  wise  that  b  5,  Fig.  115, 
are  brought  together  in  the  middle,  united,  and  seen 
single  in  Fig.  116.  But  where  ?  at  what  distance  ?  Evi- 
dently this  can  only  be  at  the  point  of  sight,  which, 
as  I  have  already  explained,  is,  in  diagrammatic  repre- 
sentations of  visual  phenomena,  where  the  common  vis- 
ual line  and  the  two  median  lines  meet  one  another  at 
the  point  JB,  Fig.  116.  Meanwhile  a  a.  Fig.  115,  will 
have  crossed  over  and  become  heteronymous,  and  their 
double  images  a  a',  Fig.  116,  will  be  seen  just  where 
their  ray-lines  E  a  and  E  a!  cut  the  median  planes,  viz., 
at  a  a'.  In  Fig.  117,  which  is  the  visual  result  when 
the  eyes  are  fixed  on  the  foreground,  the  shifting  or 
sliding  of  the  two  images  of  the  card  is  not  quite  so 
great  as  before.  It  is  only  enough  to  bring  together 
the  nearer  points  a  a.  Fig.  115,  but  not  b  b.  These 
latter,  therefore,  are  homonymously  double.  The  united 
images  of  a  a  are  seen  single  on  the  common  visual  line, 
and  at  the  distance  A  where  the  double  images  of  the 
median  line  cross  each  other;  while  b  b  are  seen  ho- 
monymously double,  and  at  b  b',  the  intersection  of 
their  ray-lines  with  the  continuation  of  the  median  lines 
after  crossing ;  for  homonymous  images  are  always  re- 
ferred beyond  the  point  of  sight. 

The  mode  of  representing  combinations  with  the 
naked  eyes  by  squinting  is  similar.  Of  course  the  place 
of  the  combined  picture  will  in  this  case  be  between 
the  eyes  and  the  card.  I  reproduce  (Fig.  118),  for  the 
sake  of  comparison,  the  usual  mode  of  representation 
from  page  139.  In  order  to  make  the  perspective  nat- 


244 


DISPUTED  POINTS  IN  BINOCULAR  VISION. 


ural,  it  is  necessary,  as  already  explained,  to  reverse  the 
mounting.  In  Fig.  118  the  mounting  is  thus  reversed, 
as  seen  by  the  fact  that  points  in  the  foreground,  a  a, 
are  farther  apart  than  in  the  background,  J  &.  The 


usual  mode  of  representation  is  shown  in  this  figure. 
The  true  visual  result  is  shown  in  Figs.  119  and  120, 
of  which  Fig.  119  represents  the  result  when  the  ob- 
server is  regarding  the  background,  and  Fig.  120  when 
he  is  regarding  the  foreground.  It  is  seen  that  not 


ON  SOME  FUNDAMENTAL  PHENOMENA.  245 

only  does  tlie  diagram  give  truly  the  place  and  distance 
of  the  combined  image,  but  also  of  the  double  images 
by  means  of  which  perspective  is  perceived. 

It  will  be  remembered  that  double  images  may  be 
nearer  or  farther  off  than  the  point  of  sight,  but  that 
in  the  former  case  they  are  heteronymous,  in  the  latter 
homonymous.  In  this  way  we  at  once  perceive  their 
distance  in  relation  to  point  of  sight.  Now,  in  the  new 
mode  of  representation,  this  fact  is  also  indicated.  In 
both  of  the  figures  119  and  120  there  are  two  places 
where  the  ray-lines  cut  the  median  lines,  and  therefore 
where  double  images  may  be  formed ;  but  in  the  one 
case  the  images  are  heteronymous,  and  therefore  we 
refer  them  to  the  nearer  points  a  a' ;  in  the  other  case 
they  are  homonymous,  and  therefore  we  refer  them  to 
the  farther  points  £  V. 

If  stereoscopic  pictures  mounted  in  the  usual  wray 
be  combined  with  the  naked  eyes  by  squinting,  or  pic- 
tures with  reverse  mounting  be  combined  in  the  stereo- 
scope, the  perspective  will  be  inverted.  In  this  case 
the  diagrammatic  representation  is  exactly  the  same, 
except  that  the  double  images  of  points  in  the  fore- 
ground a  a'  will  now  be  homonymous,  and  therefore 
referred  to  the  other  possible  point  of  reference,  viz., 
beyond  the  point  of  sight ;  and  double  images  of  points 
in  the  background  o  bf  will  become  heteronymous,  and 
therefore  referred  to  the  nearer  point. 

Some  curious  Phenomena  illustrating  the  heteronymous 
Shifting  of  the  two  Fields  of  View. 

Experiment  1. — To  trace  a  picture  where  it  is  not. 
Take  a  postage  stamp,  or  a  piece  of  coin,  or  a  medallion, 
or  a  small  object  or  picture  of  any  kind ;  place  it  on  a 
sheet  of  white  paper.  Take  then  a  thin  opaque  screen, 


246 


DISPUTED  POINTS  IN  BINOCULAR   VISION. 


like  a  pamphlet,  or  thin  book,  or  piece  of  cardboard, 
and  set  it  upright  on  the  right  side  of  the  object  or 
picture,  and  bring  down  the  face  upon  the  top  edge  of 
the  screen,  in  such  wise  that  the  latter  shall  occupy  the 
median  plane.  If  we  now  gaze  with  the  eyes  parallel— 
i.  e.,  on  vacancy — the  median  card  will  double  and  be- 
come two  parallel  cards,  and  in  the  middle  between 
them  will  be  seen  the  object  or  picture.  With  a  pencil 
in  the  right  hand  we  may  now  trace  the  outline  of  the 
object  or  picture,  by  means  of  its  image,  on  the  right 
side  of  the  screen,  although  the  actual  object  or  picture 
is  on  the  left  side  of  the  same. 

The  accompanying  diagrams  illustrate  and  explain 
the  phenomena.  In  Fig.  121,  R  and  L  are  the  two 
eyes  looking  down  on  the  paper  sheet  sh  •  ms  is  the 
median  screen,  and  c  the  coin  on  its  left  side ;  a,  the 
spot  where  the  outlino  is  traced  with  the  poncil  P.  This 


FIG.  121. 


FIG.  122. 


figure  therefore  gives  the  actual  condition  of  things. 
The  visual  result,  and  therefore  the  explanation,  is 
given  in  Fig.  122.  By  careful  inspection  it  is  seen  that 
the  screen  is  doubled  heteronymously,  and  becomes  two 
parallel  screens  ms,  m's;  that  the  two  images  of  the 


ON  SOME  FUNDAMENTAL  PHENOMENA.  94.7 

paper  sheet  are  slidden  over  each  other,  so  that  the  left 
eye,  its  visual  line,  and  its  image  of  the  coin  c  are  all 
brought  to  the  middle,  while  the  right  eye,  its  visual 
line,  and  its  image  of  the  pencil  and  of  the  point  a  are 
also  brought  to  the  middle  from  the  other  side,  and 
superposed.  We  therefore  see  the  image  of  the  coin 
and  trace  its  outline  exactly  an  interocular  space  dis- 
tant from  its  real  position.  If  it  were  not  for  the 
screen,  there  would  be  another  (right-eye)  image  of  the 
coin  and  another  (left-eye)  image  of  the  pencil  and  of 
the  point  a.  These  I  have  indicated  in  dotted  outline. 
Experiment  2. — If  we  make  the  experiment  with- 
out the  use  of  the  median  screen,  then  the  cause  of  the 
phenomenon  becomes  obvious.  If  we  lay  a  piece  of 
money  on  a  sheet  of  paper,  and  then  gaze  in  the  direc- 
tion of  the  coin,  but  with  the  eyes  parallel — i.  e.,  on 
vacancy — the  money  of  course  separates  into  two  images 
an  interocular  space  apart.  If  we  approach  this  with  a 
pencil  for  the  purpose  of  tracing  the  outline,  we  will 
see  the  pencil  also  doubled.  If  we  now  bring  corre- 
sponding images  in  contact — i.  e.,  right-eye  image  (left 
in  position)  of  the  pencil  with  the  right-eye  image  (left 
in  position)  of  the  coin — we  touch  the  coin  with  the 
pencil.  But  if,  on  the  contrary,  we  bring  the  right-eye 
image  (left  in  position)  of  the  pencil  to  the  left-eye  im- 
age (right  in  position)  of  the  coin,  we  may  trace  the 
outlines  of  the  piece  an  interocular  space  distant  from 
its  true  position.  This  is  shown  in  Fig.  123,  which 
gives  the  visual  result  of  such  an  experiment — c  and  cf 
being  the  right-  and  left-eye  images  of  the  coin,  and 
P  and  P'  of  the  pencil.  If,  while  the  operation  is  going 
on,  we  observe  carefully,  we  will  see  to  the  right  the 
left-eye  image  of  the  pencil,  P ',  engaged  in  making  a 
tracing.  But  there  is  no  tracing  in  this  place;  it  is 


248     '      DISPUTED   POINTS  IN  BINOCULAR  VISION. 

only  the  left  eye  image  of  the  real  tracing  being  made 
by  the  other  pencil,  P.  In  the  previous  experiment  the 
screen  cuts  off  all  the  images  except  the  right-eye  image 


d 


of  the  pencil  and  the  left-eye  image  of  the  coin,  which 
are  brought  together  in  the  middle. 

Tolerably  good  tracings  of  a  picture  may  be  made 
in  this  way.  The  only  difficulty  in  making  them  really 
accurate  is  the  unsteadiness  of  the  optic  axes,  and  there- 
fore of  the  place  of  the  image.  I  have,  however,  used 
this  method  in  making  outline  tracings  of  microscopic 
objects,  which  may  be  filled  out  afterward.  For  this 
purpose  a  card  is  placed  on  the  right  side  of  the  micro- 
scope, and  the  microscopic  object  is  viewed  with  the  left 
eye,  while  the  right  eye  is  used  for  guiding  the  pencil. 
Precisely  as  in  the  experiment  with  the  coin  (Fig.  123), 
the  left-eye  image  of  the  object  and  the  right-eye  image 
of  the  pencil  and  of  a  certain  spot  on  the  card  are 
brought  together  in  the  middle. 

Experiment  3. — To  trace  the  outlines  of  a  light  on 
an  opaque  screen.  The  same  experiment  may  be  mod- 
ified in  an  interesting  way  thus :  Set  a  light  in  front  of 
you  on  a  table.  Place  a  median  screen  of  cardboard  or 
of  tin  between  the  eyes,  so  that  the  light  can  be  seen 
with  both  eyes.  Now  bend  the  screen  to  the  right  so 
as  to  make  a  right  angle  at  the  distance  of  6  or  8  inches 
from  the  eyes.  This  part  will  cut  off  the  view  of  the 


ON  SOME  FUNDAMENTAL  PHENOMENA. 


249 


candle-flame  from  the  right  eye.  Nevertheless,  while 
gazing  steadily  at  the  flame,  a  really  correct  outline  of 
it  may  be  drawn  on  the  opaque  transverse  screen, 
precisely  as  if  it  were  transparent.  This  is  illustrated 
and  explained  by  the  accompanying  diagrams.  Fig. 
124:  is  the  actual  condition  of  things.  F  is  the  flame ; 
ms,  the  median  screen,  resting  on  the  nose  n  •  ts,  the 
transverse  portion  of  the  screen.  Now,  just  where 


FIG.  124. 


FIG.  125. 


ts 


its 


ms 


•r 


n 


the  visual  line  of  the  right  eye  pierces  the  transverse 
screen,  viz.,  at  /",  we  may  draw  the  picture  of  the  flame 
F,  precisely  as  if  it  were  transparent.  The  explana- 
tion is  found  by  examining  the  visual  result,  Fig. 
125.  By  the  heteronymous  doubling  of  the  median 
and  transverse  screens,  the  left-eye  image  of  the  flame 
and  the  right-eye  image  of  the  transverse  screen  ts  are 
brought  together,  and  the  flame  may  be  seen  as  it  were 


250  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

through  the  opaque  screen  as  a  transparency,  and  drawn 
at  f.  In  order  to  show  that  the  flame  is  seen  only  by 
one  eye,  I  have  stopped  one  of  the  combined  visual 
lines  at  the  screen.  The  apparent  transparency  of  an 
opaque  screen  in  this  case  is  precisely  the  same  as  the 
transparent  borders  of  an  opaque  screen  mentioned  and 
explained  on  page  240. 

Experiment  4- — To  see  through  a  book,  a  deal  board, 
or  the  back  of  the  hand,  or  even  if  necessary  through  a 
millstone.  Roll  up  a  thin  pamphlet  into  a  hard  tube  a 
half  or  three  quarters  of  an  inch  in  diam- 
eter, and  hold  it  with  the  left  hand  be- 
tween the  thumb  and  hand,  as  shown  in 
Fig.  126.  Place  the  right  eye  to  the  end 
of  the  tube  and  look  through  the  tube  at 
the  opposite  wall,  or  still  better  at  a  map 
or  picture  hanging  on  the  wall,  while  the 
back  of  the  hand  conceals  the  map  or  pic- 
ture from  the  left  eye.  A  circular  spot  on 
the  wall  or  map  will  be  seen  through  the 
center  of  the  hand  (Fig.  126),  precisely  as  if  there  were 
a  circular  hole  in  the  hand.  Of  course  a  book  or  an 
opaque  plate  of  any  kind  may  be  substituted  for  the 
hand  in  this  experiment. 

The  explanation  is  as  follows :  The  visual  line  of 
the  right  eye  passes  through  the  axis  of  the  tube  and 
pierces  the  center  of  the  circular  visible  area  of  the 
object  regarded,  while  the  visual  line  of  the  left  eye 
pierces  the  back  of  the  hand  or  the  book  at  a  point  dis- 
tant from  the  axis  of  the  tube  just  an  interocular  space, 
or  about  2|-  inches.  By  the  right  and  left  shifting  of 
the  fields  of  view  already  explained,  the  two  visual  lines 
are  brought  together  in  the  middle ;  and  therefore  the 
center  of  the  area  regarded  by  the  right  eye  and  the 


ON  SOME  FUNDAMENTAL  PHENOMENA.  251 

spot  on  the  hand  or  book  pierced  by  the  left  visual  lino 
are  also  brought  together  and  superposed. 

One  thing  more  to  complete  the  explanation :  The 
impression  on  the  right  eye  prevails  over  that  on  the 
left  —  the  impression  of  the  circular  area  obliterates 
that  of  the  corresponding  area  on  the  hand  or  book  for 
two  reasons :  first,  because  the  circular  area  is  strongly 
differentiated  from  the  rest  of  the  right-eye  field  of 
view  (i.  e.,  the  dark  interior  of  the  tube),  while  the  cor- 
responding or  coincident  area  of  the  left-eye  field  (the 
hand  or  book)  is  not  thus  differentiated ;  and  second, 
because  both  eyes  are  focally  adjusted  for  the  distance 
of  the  object  seen  by  the  right  eye  only.  Thus  it  hap- 
pens that  the  right  eye  sees  only  the  circular  area,  the 
rest  of  its  field  being  very  dark  ;  while  the  left  eye  sees 
all  its  field  except  the  spot  corresponding  to  and  cover- 
ing the  circular  area.  Thus  the  binocular  observer  sees 
the  general  field  of  the  left  eye  (the  hand  or  book),  in 
the  middle  of  which  he  also  sees  the  circular  area  of 
the  right-eye  field.  But  if  an  ink-spot  be  made  on  the 
back  of  the  hand  or  book  just  where  the  left  visual  line 
pierces  it,  the  impression  of  this  will  be  strong  enough 
to  resist  obliteration  ;  the  strongly  differentiated  ink- 
spot  will  be  seen  in  the  center  of  the  circular  area, 
as  shown  in  Fig.  120. 


CHAPTEE  IY. 

VISUAL   PHENOMENA   IN  OCULAR   DIVERGENCE. 

THE  only  normal  condition  of  the  optic  axes  is  either 
parallelism  or  convergence.  We  can  not  voluntarily 
make  the  optic  axes  divergent,  because  there  is  no  use- 
ful purpose  subserved  by  such  a  position ;  there  would 
ba  no  meeting  of  the  optic  axes,  and  therefore  no  point 
of  sight.  All  the  advantages  of  binocular  vision  are 
conditioned  on  convergence  only.  Divergence  would 
only  confuse  by  giving  false  information.  But,  al- 
though the  power  of  divergence  could  be  of  no  use 
and  has  therefore  never  been  acquired,  yet  under  cer- 
tain circumstances  divergence  does  occur,  and  the  curi- 
ous phenomena  which  then  follow  are  an  admirable 
illustration  of  the  principles  of  binocular  vision  already 
set  forth.  We  will  give  a  few  of  these  phenomena. 

1.  In  Drowsiness. — It  is  well  known  that  in  extreme 
drowsiness,  when  we  lose  control  over  the  ocular  mus- 
cles, we  see  double  images.  It  is  universally  believed 
and  taught  by  physiologists  that  this  is  the  result  of  con- 
vergence of  the  optic  axes  in  sleep.  I  know  of  no  ob- 
servations purporting  to  prove  this.  It  is  probably  an 
inference  from  the  contracted  state  of  the  pupils  in 
sleep,  and  the  fact  that  contraction  of  the  pupils  is 


VISUAL  PHENOMENA  IN  OCULAR  DIVERGENCE.       253 

usually  consensual  with  optic  convergence.*  This  view 
is  certainly  false.  Double  images  in  sleepiness  are  cer- 
tainly due  to  divergence,  not  convergence,  of  the  optic 
axes. 

In  extreme  drowsiness  I  have  often  observed  the 
object  which  I  wras  regarding  (it  might  be  the  head  of 
a  dull  speaker)  divide  into  two  images,  which  then  sep- 
arated more  and  more,  until  at  a  distance  of  30  feet 
they  were  10  to  15  feet  apart.  Even  under  these  con- 
ditions I  have  found  it  possible  to  make  a  scientific  ex- 
periment. Often,  control  over  the  ocular  muscles  is 
lost  even  while  consciousness  and  control  over  mental 
acts  is  still  perfect.  Often,  although  by  effort  I  could 
retain  control  over  the  eyes,  I  have  chosen  to  abandon 
it  in  order  to  make  the  following  experiments. 

Experiment  1. — As  soon  as  the  images  are  well  sep- 
arated, I  wink  the  right  eye :  immediately  the  left  im- 
age disappears.  The  images  are  therefore  heieronymows. 
But  convergence  produces  homonymous  images,  while 
parallelism  and,  a  fortiori,  divergence  produce  heterony- 
mous  images.  In  this  case  the  heteronymous  images 
can  not  be  produced  by  mere  parallelism,  because  this 
state  separates  the  images  only  an  interocular  space,  or 
about  2J-  inches,  whereas  the  images  may  be  separated 
many  feet :  therefore  they  are  produced  by  divergence. 
The  amount  of  divergence  is  easily  calculated.  At  a 
distance  of  30  feet  a  separation  of  the  double  images  of 
10  feet  would  require  an  angular  divergence  of  the  optic 
axes  of  nearly  19°  ;  a  separation  of  15  feet  would  indi- 
cate an  angular  divergence  of  28°. 

*  "  In  sleep  and  in  sleepiness  both  eyes  are  turned  inward  and  up- 
ward." "The  contracted  state  of  the  irides  in  sleep  is  a  consensual 
motion  dependent  on  the  position  of  the  eyes,  which  are  turned  inward 
and  upward," — MuUcr,  "  Physiology,"  Am.  ed.,  pp,  810  and  535. 


254:          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

In  every  such  experiment  the  consciousness  is  quick- 
ly and  completely  aroused,  and  the  double  images  are 
speedily  reunited,  though  not  so  speedily  but  that  the 
result  is  unmistakable.  But,  lest  some  may  regard  the 
speedy  union  of  the  images  as  an  objection  to  this  ex- 
periment, we  will  take  another. 

Experiment  2. — While  lying  abed  in  the  morning, 
if  one  gazes  on  vacancy,  objects  near  at  hand  (say  the 
bedpost)  are  doubled  heteronymously,  the  images  being 
2^  inches  apart.  If,  while  thus  gazing  and  observing 
the  heteronymous  images,  one  should  be  overtaken  by 
drowsiness  and  consequent  loss  of  control  over  the 
ocular  muscles,  he  will  see  that  the  already  heterony- 
mous images  separate  more  and  more.  Now,  if  this 
were  due  to  convergence,  the  heteronymous  images 
would  approach,  unite,  cross  over,  and  become  homony- 
mous. 

It  is  certain,  then,  that  in  myself,  in  extreme  drow- 
siness, when  control  over  the  ocular  muscles  is  lost,  and 
therefore  presumably  in  sleep,  the  eyes  diverge.  I  have 
also  satisfied  myself  that  my  case  is  not  exceptional  in 
this  respect,  for  my  results  have  been  verified  by  several 
other  persons.  I  think,  therefore,  I  may  assume  it  as 
a  general  law. 

Double  vision  is  also  a  well-known  phenomenon  of 
extreme  intoxication.  The  unnatural  appearance  of  the 
eyes  in  such  cases  is  due  to  want  of  parallelism  of  the 
optic  axes.  I  have  on  several  occasions  examined  the 
eyes  of  those  in  this  sad  condition,  and  have  always 
found  the  axes  divergent.  This  seems  to  arise  from 
partial  paralysis  of  the  ocular  muscles. 

If  we  examine  the  eye-sockets  of  a  human  skull, 
we  find  that  their  axes  diverge  about  25°-30°.  This 
is  about  the  extreme  divergence  of  the  optic  axes  in 


VISUAL  PHENOMENA  IN  OCULAR  DIVERGENCE.       255 

drowsiness.  It  is  probable,  therefore,  that  in  a  state  of 
perfect  relaxation  or  paralysis  of  the  ocular  muscles  the 
optic  axes  coincide  with  the  axes  of  the  conical  eye- 
sockets,  and  that  it  requires  some  degree  of  muscular 
contraction  to  bring  the  optic  axes  to  a  state  of  parallel- 
ism, and  still  more  to  one  of  convergence,  as  in  every 
voluntary  act  of  sight.  In  the  human  eye,  therefore, 
and  also  in  that  of  the  highest  animals,  there  are  three 
conditions  of  the  optic  axes  :  first,  convergence,  as  when 
we  look  at  a  near  object ;  second,  parallelism,  as  when 
we  look  at  a  distant  object  or  gaze  on  vacancy ;  third, 
divergence,  when  we  lose  control  over  the  ocular  mus- 
cles, as  in  drowsiness,  in  drunkenness,  in  sleep,  and  in 
death.  The  first  requires  a  distinct  voluntary  contrac- 
tion of  the  ocular  muscles ;  in  the  second  there  is  no 
voluntary  action,  but  only  that  involuntary  tonic  con- 
traction characteristic  of  the  healthy  waking  state ;  in 
the  third  the  relaxation  is  complete.  The  first  is  the 
active  state  of  the  eye,  the  second  the  waking  passive 
state,  the  third  the  absolutely  passive  state. 

2.  Other  Modes  of  producing  Divergence.— But  the' 
divergence  of  the  optic  axes  may  be  effected  in  other 
ways.  In  most  normal  eyes  the  passive  state  is  one  of 
parallelism.  It  is  easy  therefore  to  double  hoinony- 
mously  the  images  of  an  object  at  any  distance  by  con- 
vergence, but  most  persons  would  find  it  impossible 
voluntarily  to  double  the  images  of  a  very  distant  ob- 
ject, as  for  example  a  star,  heteronymously — i.  e.,  by 
divergence.  Yet  under  certain  conditions  a  slight  di- 
vergence is  possible.  For  example,  I  find  I  can  (and 
I  believe  most  persons  can)  combine  with  the  naked  eyes 
and  with  natural  perspective  (i.  e.,  beyond  the  plane  of 
the  card)  stereoscopic  pictures  in  which  identical  points 
are  farther  apart  than  the  interocular  distance.  I  can 


256  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

not  always  succeed,  being  able  to  do  so  only  when  my 
mind  is  in  an  exceptionally  passive  state. 

Experiment  3. — I  take  now  a  skeleton  stereoscopic 
diagram,  identical  points  in  the  background  of  which 
are  separated  by  a  space  greater  by  an  eighth  of  an  inch 
than  my  interocular  space.  By  holding  it  at  arm's 
length  so  as  to  make  the  divergence  as  small  as  possi- 
ble, I  succeed  in  combining.  After  the  combination 
is  stable,  I  can  bring  the  card  nearer  and  nearer  until 
it  is  within  5  inches  of  my  eyes,  and  yet  the  combina- 
ation  is  retained.  But  this  corresponds  to  a  divergence 
of  only  1J°. 

Experiment  4- — But  by  mechanical  force  we  may 
make  the  eyes  diverge  40°  or  50°.  This  is  done  by  pres- 
sure in  the  external  corner  of  the  eye.  By  thrusting  a 
finger  of  each  hand  into  the  external  corners  of  the  eyes 
I  can  make  the  two  images  of  an  object  directly  in  front 
separate  50°,  or  the  images  of  two  objects  situated  25° 
to  the  right  and  left  of  the  median  line,  and  therefore 
50°  apart  from  each  other,  come  to  the  front  and  unit3. 

The  following  diagrams  represent  and  explain  the 
visual  phenomena  in  divergence  of  the  optic  axes. 

In  Fig.  127,  which  represents  the  actual  relation  of 
parts,  m  is  the  median  line  ;  v  v,  the  visual  lines  or  optic 
axes  produced ;  A,  an  object  on  the  median  line ;  I  ~b, 
two  similar  objects  in  the  direction  of  the  diverging 
visual  lines  ;  and  r  r,  ray-lines  from  the  object  A.  Fig. 
128  shows  the  visual  result  if  the  lines  in  Fig.  127  were 
visible  lines  drawn  on  the  plane  described  on  page  231. 
It  will  be  seen  that  by  heteronymous  shifting  and  then 
heteronymous  rotation  the  whole  diagram  represented 
by  Fig.  127  has  been  carried  and  rotated  by  the  right 
eye  to  the  position  of  the  lines  connected  by  the  un- 
primed  vinculum,  and  by  the  left  eye  to  the  position 


VISUAL  PHENOMENA  IN  OCULAR  DIVERGENCE.      257 


of  the  lines  connected  by  the  primed  vinculum.  By 
this  means  the  two  visual  lines  v  v  are  brought  together 
and  combined  as  the  common  visual  line  V,  and  two  of 
the  images  of  the  objects  J  b  are  brought  together  and 
superposed  at  B ;  the  median  line  is  doubled  and  ro- 


Fis.  12T. 

A 


I    b 


m  \r 


tated  heteronymously  to  the  positions  m  m',  carrying 
with  them  the  double  images  of  the  median  object  A 
as  a  a'.  The  above  diagram  correctly  represents  the 
position  and  the  distance  of  the  double  images  a  a',  and 
the  position  of  the  combined  image  B,  but  can  not 
represent  the  distance  of  the  combined  image,  because 
there  is  no  point  of  sight.  For  the  point  of  sight  is 
really  the  point  of  optic  convergence  or  meeting  of  vis- 
ual lines  /  in  diagrams  representing  visual  results,  it  is 
the  point  of  crossing  of  the  doubled  median  lines  /  but 
this  point,  by  both  definitions,  would  be  in  this  case  be- 
hind the  head.  The  diagram  therefore  correctly  repre- 
sents all  the  visual  facts  ;  for,  there  being  in  divergence 


258  DISPUTED  POINTS  IN  BINOCULAR  VISION. 

no  point  of  sight,  the  distance  of  objects  in  the  visual 
line  is  indeterminate  as  represented.  It  is  impossible 
by  the  usual  method  to  correctly  represent  any  of  the 
visual  facts. 

3.  If  the  Law  of  Direction  be  opposed  to  the  Law  of 
Corresponding  Points,  the  Latter  will  prevail. — These 
two  most  fundamental  laws  of  vision  are  sometimes 
in  discordance  with  each  other.  The  reason  of  this 
may  be  thus  explained :  The  law  of  direction  is  the 
fundamental  law  of  monocular  vision,  as  the  law  of 
corresponding  points  is  of  binocular  vision.  Now,  for 
each  eye,  and  therefore  for  the  monocular  observer, 
direction  is  determined  by  reference  to  the  optic  axis, 
but  for  the  binocular  observer  by  reference  to  the  me- 
dian line.  On  account  of  this  difference  of  line  of  ref- 
erence, while  objects  seen  single  are  seen  in  their  true 
positions,  double  images  are  always  seen  in  positions 
different,  and  in  some  cases  widely  different,  from  the 
object  which  they  represent.  The  difference  may  even 
amount  to  45°.  For  example :  The  binocular  field  of 
view  in  my  own  case  is  100°  in  a  horizontal  direction. 
By  strong  convergence  I  can  nearly  bring  the  double 
images  of  the  root  of  my  nose  together,  and  thus  oblit- 
erate the  common  field.  I  am  sure  therefore  that  I  can 
make  the  optic  axes  of  my  two  eyes  cross  each  other  at 
right  angles.  In  such  a  case,  of  course,  objects  directly 
in  front  are  doubled  and  their  images  separated  90° 
from  each  other,  while  objects  lying  to  the  right  and 
left  90°  from  each  other  are  brought  to  the  front  and 
their  images  superposed.  Here  the  images  are  45° 
from  the  true  position  of  the  objects  which  they  repre- 
sent. Thus,  Fig.  120  represents  the  actual  relation  of 
things  in  this  case,  and  Fig.  130  the  visual  result,  show- 
ing that  the  positions  of  the  objects  M  and  a  a  are  com- 


VISUAL  PHENOMENA  IX  OCULAR  DIVERGENCE.      259 

pletely  reversed.  It  may  indeed  be  said  that  the  case 
of  a  a  seen  in  front  may  be  reconciled  with  the  law  of 
direction.  For,  if  the  combined  images  be  referred  to 


FIG.  129. 
M 


a., 


'' 


the  point  of  optic  convergence  A,  as  indeed  they  often 
are,  then  each  eye  sees  its  own  object  in  its  true  direc- 
tion, but  only  mistakes  its  distance.  To  this  I  would 


answer  that  each  eye  does  indeed  give  the  true  direction, 
as  is  quickly  shown  by  shutting  one  of  them,  but  the 
two  eyes  together  do  not.  Each  sees  its  own  object  in 


260          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

the  true  direction,  but  the  binocular  observer  sees  their 
combination  in  a  wrong  direction.  In  the  case  of  the 
double  images  m  and  mf  of  the  object  J/,  it  is  still  more 
difficult  to  explain  their  apparent  position  by  the  law 
of  direction. 

A  curious  Corollary. — It  is  seen  that,  under  all  cir- 
cumstances, whatever  be  the  position  of  the  optic  axes, 
objects  in  the  visual  lines  are  moved  to  the  front  and 
seen  there.  Now  the  same  would  be  true  if  our  eyes 
were  turned  directly  outward  right  and  left.  There 
can  be  no  doubt  that  if  we  could  turn  our  eyes  directly 
outward,  or  if  our  eyes,  retaining  their  present  organi- 
zation and  properties  in  regard  to  corresponding  points, 
were  transferred  to  the  sides  of  the  head  with  their 
axes  straight  right  and  left — i.  e.,  making  an  angle  of 
180°  with  each  other — images  of  objects  in  the  direction 
of  these  axes,  and  therefore  directly  right  and  left,  would 
be  moved  round  90°  each,  and  combined  and  seen  di- 

FIG.  181.  FIG.  132. 


/ 

(n 


rectly  in  front.  This  seems  an  extraordinary  result, 
but  it  is  a  necessary  consequence  of  the  law  of  corre- 
sponding points.  The  retinal  images  of  the  two  objects 
are  on  corresponding  points,  viz.,  on  the  central  spots  ; 


VISUAL  PHENOMENA  IN  OCULAR  DIVERGENCE.       261 

therefore,  by  the  law  of  corresponding  points,  they 
must  be  seen  as  one.  But  where  else  can  this  take 
place  but  in  front  ?  The  accompanying  figures  are  a 
diagrammatic  representation  of  these  facts,  Fig.  131 
being  the  supposed  condition  of  things,  and  Fig.  132 
the  visual  result.  After  the  frequent  explanations  of 
similar  figures,  a  bare  inspection  will  be  sufficient. 


CHAPTER  Y. 

COMPARATIVE  PHYSIOLOGY  OF  BINOCULAR    VISION. 

THE  cause  of  the  remarkable  law  of  corresponding 
points,  on  which  all  the  phenomena  of  binocular  vision 
depend,  has  not  been  traced  with  certainty  to  anatomical 
structure.  It  is  probably  in  some  way  connected  with 
the  existence  of  an  optic  chiasm  and  the  crossing  of  the 
fibers  of  the  two  optic  nerves  there,  but  in  what  way 
is  not  understood.  We  have  already  (page  102)  alluded 
to  a  hypothesis,  "  the  nativistic  theory,"  which  supposes 
that  fibers  from  corresponding  points  unite  into  one 
fiber  or  end  in  one  brain-cell ;  but  even  if  this  be  true, 
it  is  undiscoverable.  The  optic  chiasm  doubtless  is  a 
sign  of  some  kind  of  sympathetic  relation  between  the 
two  eyes ;  but  whether  this  necessarily  reaches  the  de- 
gree which  produces  corresponding  points  is  uncertain. 

The  chiasm  exists  in  nearly  all  vertebrates,  but  not 
in  invertebrates.  In  vertebrates  sometimes  the  fibers  of 
the  two  nerve-roots  (optic  tracts)  simply  cross  each  other 
without  uniting;  this  is  the  case  in  fishes.  In  others 
the  fibers  of  the  roots  partly  cross  and  partly  do  not, 
so  that  each  nerve  is  made  up  of  fibers  from  both  roots ; 
this  is  the  case  in  mammals  and  birds,  and  probably  to 
some  extent  in  reptiles.  It  seems  certain  then  that  in- 
vertebrates do  not  enjoy  binocular  vision.  It  is  proba- 


PHYSIOLOGY  OF  BINOCULAR  VISION.  263 

ble  also,  from  anatomical  structure  alone,  that  osseous 
fishes  do  not  enjoy  this  faculty.  Whether  in  some  still 
higher  animals  the  sympathetic  relation  which  certainly 
exists  between  the  two  eyes  reaches  the  point  necessary 
for  their  successful  use  of  the  two  eyes  as  one  instru- 
ment is  also,  I  believe,  very  doubtful.  I  proceed  to  give 
some  reasons  for  this  belief,  derived  from  the  position 
of  the  twot  eyes. 

In  man  the  axes  of  the  conical  eye-sockets  diverge 
about  25°,  or  each  makes  with  the  median  line  an  angle 
of  a  little  more  than  12°.  In  these  slightly  diverging 
conical  sockets  the  eyeballs  are  so  placed,  and  the  mus- 
cles so  adjusted,  that  in  the  waking  passive  state  their 
axes  are  parallel ;  and  from  this  passive  parallel  condi- 
tion they  may  be  easily  converged  even  upon  very  near 
objects.  In  man,  then,  though  the  eye-sockets  still 
diverge  considerably,  the  eyes  are  set  in  front  with 
axes  naturally  parallel.  This  is  evidently  the  position 
most  suitable  for  binocular  vision ;  for  the  eye-sockets 
could  not  be  brought  any  nearer  to  parallelism  without 
diminishing  too  much  the  interocular  space,  and  thus 
the  accuracy  of  binocular  judgment  of  distance. 

In  monkeys  the  position  of  the  eyes  is  much  the 
same  as  in  man.  They  are  placed  well  in  front,  writh 
their  axes  apparently  parallel  in  the  passive  state,  and 
therefore  well  adapted  for  binocular  convergence  on 
near  objects.  But  as  we  go  down  the  vertebrate  scale, 
the  eyes  are  placed  wTider  and  wider  apart,  then  moved 
more  and  more  to  the  side  of  the  head ;  the  axes  of  the 
eye-sockets  are  therefore  more  and  more  divergent,  and 
the  difficulty  of  convergence  on  a  near  point  becomes 
greater  and  greater,  until  in  some  mammals,  as  cetacea, 
in  many  birds,  and  in  all  fishes,  the  eyes  are  placed  110 
longer  in  front,  but  on  the  sides  of  the  head,  with  their 
12 


264          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

optic  axes  inclined  nearly  or  quite  180°  with  each  other. 
It  is  evident  that  animals  with  eyes  so  placed  can  not 
converge  the  optic  axes  on  a  single  point,  especially  a 
near  point.  In  fact,  it  is  well  known  that  those  birds 
which  have  their  eyes  placed  well  on  the  side  of  the 
head,  when  they  wish  to  look  attentively,  turn  the  head 
and  look  with  one  eye.  It  seems  impossible  that  animals 
like  the  whale  and  fishes,  in  which  the  eyes  are  fairly 
on  the  side  of  the  head,  can  enjoy  a  true  binocular  vision 
with  its  consensual  movements  of  the  two  eyes,  with  its 
double  and  combined  images,  its  stereoscopic  effects, 
and  its  complex  but  accurate  visual  judgments  based 
on  these  effects.  It  seems  impossible  that,  for  such 
animals,  the  law  of  corresponding  points  could  have 
been  developed,  or  can  now  exist ;  for  if  it  did,  it  could 
only,  as  we  have  seen  (page  260),  lead  to  false  judg- 
ments as  to  the  direction  of  objects.  They  see  with  two 
eyes,  but  these  do  not  act  together  as  one  instrument, 
as  a  single  binocular  eye ;  they  are  independent,  and  see 
each  for  itself.  I  have  watched  the  motions  of  the  eyes 
of  fishes  swimming  in  an  aquarium,  and  they  seem  to 
me  to  move  independently  of  each  other.  The  same 
is  true  of  all  other  senses,  even  in  man  :  however  much 
their  organs  may  be  multiplied,  each  organ  perceives 
for  itself.  The  property  of  corresponding  points,  from 
which  all  the  phenomena  of  binocular  vision  are  de- 
rived, is  something  peculiar  to  the  eye  of  the  higher 
animals.  Nothing  analogous  exists  in  the  other  senses. 
Binocular  vision  in  its  perfection,  as  it  exists  in  man 
and  the  higher  animals,  is  the  last  result  of  the  gradual 
improvement  of  that  most  refined  of  all  the  sense-or- 
gans, the  eye,  specially  adapting  it  to  meet  the  wants 
of  the  higher  faculties  of  the  mind. 

There  are,  it   is  true,  consensual  movements  and 


PHYSIOLOGY  OF  BINOCULAR  VISION.  265 

sympathetic  relations  in  the  double  organs  of  other 
senses — e.  g.,  the  consensual  movements  of  the  hands. 
There  is  even  a  kind  of  binaural  audition,*  by  means 
of  which  we  judge  imperfectly  of  direction  of  sound. 
But  these  are  not  only  infinitely  inferior  in  degree  of 
perfection  to,  but  they  are  essentially  different  in  kind 
from,  that  consensual/ movement  and  that  sympathetic 
relation  which  wre  find  in  the  eyes,  and  which  slowly 
in  the  process  of  evolution  gave  rise  to  the  wonderful 
property  of  corresponding  points  and  the  phenomena 
of  binocular  vision. 

Binocular  vision,  then,  is  certainly  wanting  in  in- 
vertebrates, for  the  eyes  in  these  are  either  immovably 
fixed,  as  in  insects  and  many  crustaceans,  or,  if  movable, 
as  in  snails,  etc.,  their  movements  are  not  consensual. 
;  The  most  perfect  eyes  among  invertebrates  are  found 
in  cephalopods.  These  have  true  recti  muscles  for 
turning  them  about,  but  from  their  position  they  can 
not  move  consensually.  There  is  also  no  optic  chiasm 
in  any  invertebrate. 

Teleost  fishes  do  not  enjoy  binocular  vision,  for 
there  is  in  them  no  optic  chiasm,  and  the  position  of 
their  eyes  makes  it  impossible  for  them  to  converge 
their  axes  on  objects,  especially  near  objects.  The 
movements  of  their  eyes  also  seem  to  be  independent. 
Sharks  and  selachians  generally  have  an  optic  chiasm, 
and  therefore  probably  more  sympathetic  connection 
between  the  eyes  than  osseous  fishes.  It  is  possible 
that  binocular  effects  begin  first  to  be  developed  in 
these.  Yet  not  only  in  these,  but  even  in  reptiles  and 
some  birds,  binocular  seems  to  be  at  least  subordinate 

*  Thompson,  "  Philosophical  Magazine,"  vol.  iv,  p.  274  (1877) ;  vol. 
vi,  p.  383  (1878);  "American  Journal  of  Science  and  Arts,"  vol.  xix,  p. 
145  (1880) ;  Steinhauser,  "  Philosophical  Magazine,"  vol.  vii,  p.  261  (1879). 


266          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

to  monocular  two-eyed  vision  (if  I  may  be  allowed  the 
expression).  The  carnivorous  birds  and  all  mammals 
except  cetacea  seem  to  enjoy  binocular  vision  very  much 
as  man  does,  though  I  believe  in  a  less  perfect  degree. 

There  is  another  peculiarity  of  the  human  eye,  prob- 
ably closely  connected  with  the  highest  effects  of  bin- 
ocular vision,  which  still  more  quickly  disappears  as  we 
go  down  the  vertebrate  scale.  I  refer  to  the  existence 
of  the  central  spot  of  the  retina.  We  have  already  seen 
that  this  spot,  situated  exactly  in  the  center  of  the  ret- 
inal concave,  and  therefore  just  where  the  visual  line 
pierces  the  retina,  is  the  most  highly  organized  and 
sensitive  portion  of  the  retina.  It  is  not  more  than  a 
millimetre  in  diameter.  Now  every  spot  of  the  retina 
has  its  representative  in  the  field  of  view.  The  repre- 
sentative of  this  is  the  point  of  sight  and  a  very  small 
area  about  that  point,  viz.,  the  area  of  very  clear  vision. 
At  the  ordinary  reading  distance  of  12  inches,  this  area 
is  not  more  than  three  quarters  of  an  inch  in  diameter. 
If,  while  gazing  steadily  and  attentively  at  one  point,  we 
observe  the  relative  distinctness  of  points  in  other  por- 
tions of  the  field  of  view,  we  shall  find  that  these  be- 
come rapidly  less  and  less  distinct  as  the  point  is  more 
distant  from  the  line  of  sight.  In  other  words,  there 
is  a  regular  gradation  of  distinctness,  from  the  point  of 
sight,  where  it  is  greatest,  to  the  extreme  margins  of 
the  field  of  view,  where  it  is  least.  Now,  as  the  retina 
corresponds  to  the  field  of  view  point  for  point,  it  fol- 
lows that  there  is  a  regular  gradation  in  keenness  and 
definiteness  of  perception,  and  therefore  in  fineness  of 
organization,  from  the  central  spot,  where  it  is  greatest, 
to  the  anterior  margin  of  the  retina,  where  it  is  least. 
This  superior  fineness  of  organization  has  not  been 
demonstrated  except  for  the  central  spot ;  but  the  gra- 


PHYSIOLOGY  OF  BINOCULAR  VISION.  267 

dation  of  distinctness  of  vision  is  its  representative,  and 
therefore  its  sign,  in  the  field  of  view. 

Now,  as  we  go  down  the  vertebrate  scale,  the  cen- 
tral spot  is  found  only  in  the  higher  monkeys.  After 
a  total  absence  in  all  other  mammals  and  all  birds,  it  is 
said  to  reappear  in  some  lizards,  especially  the  chame- 
leon. But  whether  in  these  the  organization  of  this 
spot  is  similar  to  that  in  man — whether  it  is  really  a 
central  spot  in  the  same  sense,  and  has  the  same  sig- 
nificance in  vision  or  not — may  be  still  a  question.  It 
seems  fair  to  conclude,  therefore,  that  the  graduation 
of  distinctness  toward  the  point  of  sight,  and  the  limi- 
tation of  the  greatest  distinctness  to  that  point,  which 
we  find  in  man,  do  not  exist,  at  least  to  the  same  de- 
gree, in  most  of  the  lower  animals. 

The  importance  of  a  central  spot  in  the  highest  ani- 
mals, and  especially  in  man,  is  very  evident.  The  lim- 
itation of  the  greatest  distinctness  to  the  point  of  sight 
is  absolutely  necessary  to  the  concentration  and  limita- 
tion of  the  most  thoughtful  attention  to  that  point.  If 
all  portions  of  the  retina  were  similarly  organized,  and 
therefore  all  points  in  the  field  of  view  equally  distinct, 
it  would  be  impossible  to  fix  the  attention  steadily  and 
thoughtfully  on  any  one  point  to  the  exclusion  of  oth- 
ers. We  might  see  equally  well,  and  over  a  wider 
area ;  but  we  could  not  look  attentively  at  anything ; 
we  could  not  observe  thoughtfully.  But  in  the  lower 
animals,  especially  those,  as  the  ruminants,  which  are 
preyed  upon  by  others,  it  is  far  more  important  to  see 
well  in  every  direction,  than  to  fix  attention  exclu- 
sively on  one  point ;  therefore  the  advantages  of  ex- 
quisite microscopic  distinctness  of  the  center  of  the 
field  is  sacrificed  for  the  much  greater  advantages  of 
moderate  distinctness  over  a  very  wide  field.  The  most 


268          DISPUTED  POINTS  IN  BINOCULAR  VISION. 

important  thing  for  them  is  a  very  wide  field  and  the 
equal  distribution  of  attention  over  every  part.  Hence 
their  eyes  are  prominent,  set  wide  apart  on  the  margins 
of  a  broad  front,  and  destitute  of  central  spot ;  so  that 
they  sweep  the  whole  horizon,  and  see  all  parts  with 
nearly  equal  distinctness. 

It  may  be  said  that  the  sight  of  these  animals  is 
equal  or  even  superior  to  that  of  man,  and  therefore  the 
organization  of  their  retina  is  probably  as  fine  as  that 
of  our  central  spot.  I  answer  that  there  are  two  things 
to  be  considered  in  this  connection.  The  one  is  sensi- 
tiveness to  light,  and  therefore  perception  of  the  pres- 
ence of  objects  /  the  other  is  distinctness  of  the  percep- 
tion of  form.  The  one  gives  us  notice  of  the  existence 
of  objects,  the  other  gives  us  distinct  knowledge  con- 
cerning these  objects.  It  is  this  latter  which  depends 
on  the  fineness  of  organization  of  the  bacillary  layer. 
Other  portions  of  the  human  retina  are  even  more  sen- 
sitive to  light  than  the  central  spot,  as  is  shown  by  the 
well-known  fact  that  we  see  a  faint  star  by  looking  a 
little  way  from  it,  when  we  can  not  see  it  by  looking 
directly  at  it.  But  distinctness  of  form  is  perceived 
only  by  the  central  spot.  It  seems  probable,  therefore, 
that  animals  destitute  of  a  central  spot,  although  they 
may  have  a  more  delicate  perception  of  the  existence 
of  objects  in  the  field  of  view  than  we,  yet  do  not  see 
the  form  of  objects  regarded  as  distinctly  as  we  do.  For 
this  reason  they  are  more  apt  to  mistake  the  nature  of 
objects,  and  therefore  more  easily  frightened  by  trifling 
causes. 

Again,  it  is  well  to  observe  that  the  chameleon,  in 
which  the  central  spot  seems  to  reappear,  is  an  animal 
whose  habits  and  mode  of  taking  its  food  require  the 
most  fixed  and  undivided  attention. 


PHYSIOLOGY  OF  BINOCULAR  VISION.  269 

The  close  connection  of  the  central  spot  with  bin- 
ocular vision  is  also  quite  evident.  The  central  spot, 
more  than  all  other  portions  of  the  retina,  is  endowed 
with  the  properties  of  corresponding  points ;  and  the 
somewhat  complex  binocular  judgments  expressed  bj 
the  term  "  stereoscopic  perspective "  are  accurate  and 
reliable  only  at  and  in  the  vicinity  of  the  point  of  sight. 
This  fact  constitutes  the  great  difficulty  in  the  way  of 
the  experimental  determination  of  the  horopter,  as  al- 
ready explained  (page  197).  It  is  therefore,  to  say  the 
least,  doubtful  if  animals  whose  eyes  want  the  central 
spots  are  able  to  judge  as  accurately  of  the  relative  dis- 
tance and  the  solid  forms  of  near  objects  as  we  do. 

The  following,  then,  are  the  general  changes  in  the 
vertebrate  eye  as  we  go  up  the  scale  :  1.  A  gradual 
change  of  the  position  of  the  eyes  from  the  sides  to  the 
front  of  the  head,  and  a  consequent  change  of  the  angle 
of  inclination  of  the  optic  axes  from  180°  to  parallel- 
ism ;  2.  A  regularly  increasing  graduation  in  the  fine- 
ness of  the  bacillary  layer  of  the  retina,  and  therefore 
in  the  accuracy  of  the  perception  of  form,  from  the 
anterior  margins  toward  the  central  parts,  so  as  finally 
to  form  in  monkeys  and  in  man  a  specially  organized 
central  spot  /  3.  A  gradually  increasing  power  of  con- 
verging the  optic  axes  on  a  single  near  point,  so  that 
the  images  of  that  point  may  fall  on  the  central  spots 
of  both  eyes ;  4.  The  gradual  evolution  of  the  proper- 
ties of  corresponding  points,  and  therefore  of  all  the 
distinctive  phenomena  of  binocular  vision. 

These  changes  seem  all  intimately  connected  with 
each  other  and  with  the  development  of  the  higher 
faculties  of  the  mind. 


INDEX. 


PAGE 

A 

Aberration . .  .  81 

reduction  of 36 

Accommodation 41 

experiment  illustrating 42 

Adjustment  for  light 37 

—  for  distance 40 

loss  of 50 

theory  of 44 

Analogues  of  double  images  in  other 

senses 95 

Aqueous  humor 24 

Astigmatism 52 

Auditive  nerve .12 


Bacillary  layer 55,  86 

Back  of  the  hand,  to  see  through 250 

Binocular  combinations,  by  the  stereo- 
scope    134 

field 91 

perspective 120,  143, 144 

perspective,   experiments    illus- 
trating   120-124 

perspective,  theories  of 145 

—  perspective,  Wheatstone's  theo- 
ries of 145-147 

perspective,  Briicke's  theory  of. .  147 

—  perspective,  experiment  illustrat- 
ing Briicke's  theory 147 

perspective,  Dove's  experiment. .  145 

perspective,  Helmholtz's,  the  true 

theory  of. 151 

perspective,  judgment  by  means 

of 156 

vision 90 

—  vision,  disputed  points  in 164 

vision,  fundamental  phenomena 

usually  overlooked  in 213 


PAGE 

Binocular  vision,  usual  mode  of  repre- 
senting untrue 214 

vision,  experiments    illustrating 

the  false  mode  of  representing 215 

vision,  comparative  physiology  of  262 

vision,  extreme  divergence  of  eye- 
sockets  incompatible  with 264 

vision  first  developed  in  sharks 

and  selachians 265 

visual  phenomena  in  ocular  di- 
vergence   252 

visual  phenomena  in  drowsiness.  252 

visual  phenomena  in  intoxication .  254 

Blind  spot 59,  78 

—  spot,  experiments  illustrating.. 73-81 
spot,  size  of 81 

—  spot,  representative  in  the  visual 
field  of  the 82 

Book,  to  see  through 250 

Brief  statement  of  laws 229 


Central  spot  of  the  retina,  properties 

of 73 

spot  of  the  retina,  function  of  the.    74 

spot  of  the  retina 266 

spot  of  the  retina  found  in  mon- 
keys   267 

spot  of  the  retina,  absence  in  mam- 
mals and  birds 267 

spot  of  the  retina  in  lizards 267 

spot  of  the  retina,  importance  of.  267 

spot  of  the  retina,  size  of 266 

Cephalopods,  eyes  of 265 

Chore-id  coat 22 

Chromatism,  correction  of 31 

correction  of,  hint  for 35 

Ciliary  processes '.     22 

Colors,  perception  of 59 


272 


INDEX. 


Colors,  primary 

—  r—  Brewster's  view  of 

-  Young's  view  of 

-  Bering's  view  of 


PAGE 

60 

60 
60 
60 


Color  blindness  .....................     62 

-  blindness,  theory  of.  ............     C3 

Combination  of  images  of  different  ob- 

jects ..............................  10S 

--  of  images  of  dissimilar  objects  .  .  .  108 

-  of  images  of  similar  objects  .....  112 

-  of  images  of  many  similar  objects  115 
Conjunctiva  .........................     18 

Consensual  adjustments  .............  104 

-  adjustments,  dissociation  of  .....  117 

-  adjustments,  dissociation  of,  ex- 
periments illustrating  .............  118 

Convergent  motion,  laws  of  ..........  177 

-  motion,  difficulty  in  experiment- 
ing on  ............................  178 

-  motion,  experiments  showing  ro- 
tation on  optic  axis  in  .........  180-187 

Cornea  ...........................  21,  22 

Corresponding  points  of  the  two  reti- 
na; ..........  ...  ................  72,96 

-  points  of  the  two  retinae,  law  of 

97,  105 

-  points  of  tho  retinae,  relation  of 
the  optic  chiasm  to  the  law  of  .....  101 

-  points  of  the  retinae,  cause  of  law 

of  ................................  262 

Crystalline  lens  .....................    23 


Daltonism 62 

Deal  board,  to  see  through  a 250 

Dcxtrality 94 

Dispersion 32 

Divergence  of  eye-sockets 2C3 

of  eye-sockets,  extreme 263, 2C4 

Double  images 92 

images,  experiments  illustrating 

92,  S3 
E 

Ectoderm 11 

Emmetropy 46 

Endoderm 11 

Erect  vision 63 

Experience,  inherited 104 

Experiments  illustrating  ihe  combina- 
tion of  images  of  dissimilar  objects, 

103-112 


PAGE 

Experiments  illustrating  the  combina- 
tion of  images  of  similar  objects  112-115 

illustrating   the    combination   of 

images  of  many  similar  objects  reg- 
ularly arranged 115-117 

Eye,  an  optical  instrument 30, 162 

defects  as  an  optical  instrument 

ofthe 46 

muscles  ofthe 18 

comparison  of  the  camera  with 

the 30,152 

adjustment  of  the 50 

ball \ 20 

ball,  contents  of 23 


Form 160 

outline 160 

solid 160 

Formation  of  the  image 24 

conditions  of  perfect  image 25 

experiment 27 

illustrations 27 

diagram    showing    formation  of 

image 28 

Fovea  centralis 57,  73 

Function  of  the  retina  . .  .64 


General  changes  in  the  eye  as  we  as- 
cend the  vertebrate  scale 269 

conclusions 118 

sensibility  related  to  special  sense 

9-15 

structure  of  human  eye 17 

Gradation  among  senses 11 

in  kind  of  contact 13 

—  in  distance  of  perception 13 

in  refinement  of  organ 14 

H 

Helmholtz's  view  as  to  the  relation  of 

apparent  and  real  vertical  meridian  197 

views,  experiments  testing..  197-202 

Heteronymous  shifting  of  the  two 

fields  of  view 216 

shifting  of  the  two  fields  of  view, 

experiments  illustrating 216-222 

shifting  of  the  two  fields  of  view, 

statement  of  the  law  of 223 

shifting  ofthe  two  fields  of  view, 

cuiious  phenomena  resulting  from.  245 


INDEX. 


273 


PAGE 

Homonymous   rotation    of  the   two 

fields 224 

rotation  of  the  two  fields,  experi- 
ments illustrating 224-227 

rotation  of  the  two  fields,  state- 
ment of  the  law  of ' 228 

Horopter,  definition  of 101, 193 

Meissner's    investigations    with 

the 169,202 

different  opinions  as  to  the  nature 

ofthe 193 

Claparede's  view  ofthe 194 

—  Helmholtz's  conclusions  regard- 
ing the 195 

confirmation    by  the  author  of 

Meissner's  views  of  the 20c-2 1 0 

conclusions  in  regard  to  the 210 

difference  between  the  author's 

and  Meissner's  view  of  the 211 

Horopteric  circle  of  Miiller 99,  194 

Human  eye,  general  structure  of IT 

muscles  of  the 18 

Humor,  aqueous ...   24 

vitreous 24 

Hypermetropy 51 


Identical  points 98 

Image,  light 152, 158 

—  invisible 152, 153 

visible 153 

formation  of 24 

conditions  of  a  perfect 25 

Images,  heteronymous 95, 100,  151 

homonymous 95,  100,  151 

Interocular  space,  determination  of. .  230 

Inverse  perspective 135 

—  perspective,  experiments  illustrat- 
ing   136-141 

Iris...  21 


Judgments  of  distance 156 

of  size , 157 

of  size,  experiments  illustrating 

157-159 

of  form 160 

gradations  of 160 

visual 161 

intellectual...  ..  161 


PAGE 

L 

Law  of  differentiation 10 

of  fatigue 70 

of  direction 85, 105 

of  direction,  illustrations  of  the  86-S9 

of  direction,  opposed  to  the  law 

of  corresponding  points 258 

- —  of  outward  projection  of  retinal 

impressions 64 

of  outward  projection  of  retinal 

impressions,  illustrations  of 66 

of  Listing 164,174,191,  197 

Laws  of  ocular  motion 164 

of  parallel  motion 164, 177 

of  convergent  motion 177 

brief  statement  of  two 229 

experiments  illustrating  new  231-237 

of  parallel  and  convergent  motion 

compared 189, 190 

Layers  of  the  retina 55 

of  the  retina,  functions  of 58 

Lens,  crystalline 28 

capsule  of 23 

opacity  of 24 

property  of  a 27 

achromatic 34 

plano-convex 34 

Linings 22 

Listing's  law 164,  174,  191 ,  197 

M 

Macula  centralis 73 

lutea 74 

Meissner's  investigations  with  the  ho- 

ropter 202 

results  with  the  horopter 204 

Mesoderm 11 

Millstone,  to  see  through  a 250 

Minimum  visibile 76 

tactile 77 

Monocular  vision 17 

vision,  explanation  of  phenomena 

of 53,  C4 

Muscse  volitantes 67 

Muscles,  straight 18 

superior 18 

inferior 18 

external 18 

internal  rectus 18 

—  oblique 19 

illustrations  of  actions  of . . .  .  19 


274 


INDEX. 


PAGE 

Myopy 46 

a  structural  delect 50 

N 

Nativistic  theory 262 

Near-sightedness 46 

Nerves,  olfactive 10 

optic 10 

auditive 10 

gustati  ve 10 

Nodal  point .  29 


Ocular    divergence,   binocular    visual 

phenomena  in 252 

divergence,  other  modes  of  pro- 
ducing   255 

—  spectrae 69 

(Eil  cyclopienne 222,  229,  231 

Old-sightedness 48 

Opposition  of  law  of  direction  to  law 

of  corresponding  points 258 

of  law  of  direction  to  law  of  cor- 
responding  points,  explanation   of 

253-2(50 

Optic  chiasm 54 

chiasm  related  to  corresponding 

points 101 

chiasm  in  lower  animals 262 

chiasm  not  found  in  invertebrates 

262,  265 

chiasm  found  in  sharks  and  sela- 
chians    265 

nerve 13 

Outline  of  a  picture,  to  trace 245 

of  a  candle-flame,  to  trace 243 


Parallel  motion,  laws  of 164 

motion,  laws  of,  experiments  il- 
lustrating   164-172 

motion,  statement  of  the  laws  of 

173, 174 

motion,    Ilelmholtz's    contrary 

statement  of  the  laws  of 1 75 

Perception  of  color 59 

Periscopism 37 

Perspective,  different  forms  of 142 

aerial 142,  144,157 

mathematical 142,  144, 157 

monocular 142,  144 

focal 142,  144, 1£6 


PAGE 

Phosphenes 67 

Point  of  sight 192 

Presbyopy , 43 

a  functional  defect 50 

Primary  visual  plane  defined ...   179 

Properties  of  central  spot 73 

Pupil 21 

Purkinje's  figures 63 

E 

Kate  of  transmission  of  nerve  impres- 
sions        9 

Relation  of  general  sensibility  to  spe- 
cial sense 9 

Eetina 22 

structure  of 53, 162 

cut,  showing  section  of 55,  56 

rods  and  cones  of 57 

function  of 64 

central  spot  of  the 226 

Retinal    and     spatial    corresponding 

points 72,162 

impressions,  law  of  outward  pro- 
jection of 64 

Retrospect 162 

Rotation,  only  apparent 176 

on  the  optic  axis 176 

real 178 

effect  of  elevation  and  depression 

of  the  visual  plane  on 1S8 

experiments  illustrating 188 

cause  of  the 189 

Meissncr's  experiments  on 189 


Sclerotic  coat 20 

Sensation,  general 9 

Sense-organ 14 

Senses,  gradation  of 11 

Sensory  nerve-fibers 9 

Sight  compared  with  other  senses. .  65,  84 

Simple  sensations 15 

Single  vision 95 

vision,  conditions  of. 97, 98 

Squinting .- 20 

Stereoscopy 125 

Stereoscopic  pictures 126 

—  pictures,  method  of  taking 127 

—  pictures,  combination  of 12S 

pictures,  combination  with  the 

naked  eye  of 128 


INDEX. 


275 


PAGE 

Stereoscopic  pictures,  experiments 
illustrating  combination  with  the 
naked  eye  of. 129-133 

phenomena,  application  of  new 

mode  of  representation  to 238 

Sub-systems,  conscio-voluntary 11 

sensori-motor 11 


reflex 

ganglionic 

Superposition  of  external  images . 

System,  nutritive 

nerve 

blood... 


11 
11 
107 
10 
10 
10 


Theories  of  the  origin  of  the  law  of 

corresponding  points 102-104 

Theory,  adjustment 44 


PAGE 

Theory,  nativistic 1C3 

empiristic 103 

of  color  perception 61 

of  color  perception,  Young's 61 

—  of  color  perception,  Stanly  HalPs  61 

Torsion 177 

Transmission  of  nerve  impressions, 

rate  of 9, 12, 13 

Two  eyes,  a  single  instrument 90 


View  of  Briicke 103 

of  Giraud-Teulon 103 

of  Helmholtz. 103 

ofMuller 103 

of  Pictet 103 

of  Prevost 103 

Vitreous  humor 24 


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THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


,,P475  Le 

L4t 

1881 


Qonte, 
ight-. 


361 


361 


